junjiehe/SkillCompiler
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity
Files
439cad87d92237e9f050ef2a139261ed1e693568
SkillCompiler/data/format-preference/natural-instructions/tasks/task1424_mathqa_probability.json
T
junjiehe 439cad87d9 Initial commit
2026-09-04 14:58:42 +08:00

4067 lines
234 KiBLFS
JSON
Raw Blame History

This file contains ambiguous Unicode characters
This file contains Unicode characters that might be confused with other characters. If you think that this is intentional, you can safely ignore this warning. Use the Escape button to reveal them.
{
"Contributors": [
"Siddhartha Mishra"
],
"Source": [
"mathqa"
],
"URL": [
"https://math-qa.github.io/math-QA/"
],
"Categories": [
"Question Answering"
],
"Reasoning": [
"Quantitative Reasoning",
"Numerical Reasoning",
"Mathematics -> Combinatorics"
],
"Definition": [
"In this task, you need to provide the correct option for a given problem on probability from the provided options."
],
"Input_language": [
"English"
],
"Output_language": [
"English"
],
"Instruction_language": [
"English"
],
"Domains": [
"Mathematics"
],
"Positive Examples": [
{
"input": "Problem: in a throw of a coin find the probability of getting a tail ? \nOptions: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 2 / 5 , e ) 2 / 7",
"explanation": "\"s = { h , t } e = { t } p ( e ) = 1 / 2 answer is a\"",
"output": "a"
},
{
"input": "Problem: a jar contains only red , yellow , and orange marbles . if there are 3 red , 6 yellow , and 4 orange marbles , and 3 marbles are chosen from the jar at random without replacing any of them , what is the probability that 2 yellow , 1 red , and no orange marbles will be chosen ? \nOptions: a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 5 / 22",
"explanation": "\"i started by finding the 2 probabilities , without calculation , like this : p ( yyr ) p ( yry ) p ( ryy ) i calculated the first one and ended in 1 / 22 . i looked at the answer choices at this point and saw answer d : 3 / 22 . this helped me realise that for the 3 possible orderings the probabbility is the same . so , it should be ( 1 / 22 ) * ( 6 ) , which indeed is 6 / 22 . e\"",
"output": "e"
}
],
"Negative Examples": [
{
"input": "Problem: if 4 people are selected from a group of 7 married couples , what is the probability that none of them would be married to each other ? \nOptions: a ) 1 / 33 , b ) 2 / 33 , c ) 1 / 3 , d ) 16 / 33 , e ) 47 / 84",
"explanation": "\"if we are to select 4 people from 7 couples without any restriction , how many ways can we make the selection ? 14 ! / 4 ! 10 ! = 1001 if we are to select 4 people from 7 couples with restriction that no married couple can both make it to the group , only a representative ? 7 ! / 4 ! 3 ! = 35 but we know that to select a person from each couple , take 2 possibilities 35 * 2 * 2 * 2 * 2 = 560 probability = desired / all possibilities = 560 / 1001 = 47 / 84 answer : e\". Hence, option b is incorrect.",
"output": "b"
},
{
"input": "Problem: there are 20 students in a class . in how many different ways can a committee of 3 students be formed ? \nOptions: a ) 650 , b ) 730 , c ) 980 , d ) 1140 , e ) 1480",
"explanation": "\"20 c 3 = 20 * 19 * 18 / 6 = 1140 the answer is d .\". Hence, option a is incorrect.",
"output": "a"
}
],
"Instances": [
{
"id": "task1424-a48e5863297941109c564a2baa797f36",
"input": "Problem: a bag contains 6 black and 4 white balls . one ball is drawn at random . what is the probability that the ball drawn is white ? \nOptions: a ) 3 / 4 , b ) 2 / 5 , c ) 1 / 7 , d ) 1 / 8 , e ) 4 / 3",
"output": [
"b"
]
},
{
"id": "task1424-6096479515f9484292e29c523aa7d9d1",
"input": "Problem: how many different ways can 2 students be seated in a row of 4 desks , so that there is always at least one empty desk between the students ? \nOptions: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 12",
"output": [
"d"
]
},
{
"id": "task1424-959514af278f494187656759107007c7",
"input": "Problem: a question paper has 2 parts , a & b , each containing 5 questions . if a student has to choose 3 from part a & 4 from part b , in how many ways can he choose the questions ? \nOptions: a ) 50 , b ) 100 , c ) 152 , d ) 150 , e ) 55",
"output": [
"a"
]
},
{
"id": "task1424-a51bcae34b7d444080008e5a48cc2ae6",
"input": "Problem: seven 6 faced dice are thrown together . the probability that all the three show the same number on them is ? \nOptions: a ) 1 / 32 , b ) 1 / 46656 , c ) 1 / 33 , d ) 1 / 38 , e ) 1 / 34",
"output": [
"b"
]
},
{
"id": "task1424-b0b7a894a5d64ebba66468b9624cdccd",
"input": "Problem: there are 11 boys and 10 girls in a class . if three students are selected at random , in how many ways that 3 girl & 2 boys are selected ? \nOptions: a ) 6600 , b ) 1300 , c ) 6780 , d ) 1976 , e ) 2448",
"output": [
"a"
]
},
{
"id": "task1424-b78434caa5f446f1974d5f0e0bde52dd",
"input": "Problem: how many cubes of 5 cm edge can be cut out of a cube of 15 cm edge \nOptions: a ) 36 , b ) 232 , c ) 27 , d ) 48 , e ) none of these",
"output": [
"c"
]
},
{
"id": "task1424-4b501c8d76b44eae8aceaea8cc276f46",
"input": "Problem: there are 9 pairs of socks and 2 socks are worn from that such that the pair of socks worn are not of the same pair . what is the number of pair that can be formed . \nOptions: a ) 62 , b ) 70 , c ) 72 , d ) 71 , e ) 76",
"output": [
"c"
]
},
{
"id": "task1424-03f8ff3b924045e6b5bf8a164138f66f",
"input": "Problem: when tossed , a certain coin has equal probability of landing on either side . if the coin is tossed 5 times , what is the probability that it will land on either side all 5 times ? \nOptions: a ) 1 / 5 , b ) 1 / 10 , c ) 1 / 12 , d ) 1 / 16 , e ) 1 / 32",
"output": [
"d"
]
},
{
"id": "task1424-075dba2c6c1e4eeb8a6eabad08492ef8",
"input": "Problem: a question paper has 2 parts , a & b , each containing 10 questions . if a student has to choose 8 from part a & 5 from part b , in how many ways can he choose the questions ? \nOptions: a ) 1100 , b ) 1200 , c ) 1235 , d ) 1354 , e ) 1140",
"output": [
"e"
]
},
{
"id": "task1424-ec762209e885441d9e34133e346ff2bc",
"input": "Problem: if two integers x , y ( x > y ) are selected from - 10 to 10 ( inclusive ) , how many possible cases are there ? \nOptions: a ) 150 , b ) 180 , c ) 190 , d ) 210 , e ) 240",
"output": [
"d"
]
},
{
"id": "task1424-60ba622e142f41c88e6ae58fc62979c3",
"input": "Problem: in 15 year ’ s time the combined age of my 4 brothers will be 107 . what will it be in the 6 year ’ s time ? \nOptions: a ) 61 , b ) 78 , c ) 71 , d ) 68 , e ) 94",
"output": [
"c"
]
},
{
"id": "task1424-6a90604c42714903b170bbebd367ef4b",
"input": "Problem: how many different ways can 2 students be seated in a row of 6 desks , so that there is always at least one empty desk between the students ? \nOptions: a ) 2 , b ) 3 , c ) 4 , d ) 20 , e ) 12",
"output": [
"d"
]
},
{
"id": "task1424-020737ca1dc245ffa2a9dde4cffb409c",
"input": "Problem: find the probability that a number selected from numbers 1 , 2 , 3 , . . . , 40 is a prime number , when each of the given numbers is equally likely to be selected ? \nOptions: a ) 10 / 40 , b ) 12 / 40 , c ) 8 / 40 , d ) 3 / 40 , e ) 7 / 40",
"output": [
"b"
]
},
{
"id": "task1424-44a5fcfc15c64872876155fd35f9bc4e",
"input": "Problem: two unbiased coins are tossed . what is the probability of getting two heads ? \nOptions: a ) 1 / 2 , b ) 1 / 4 , c ) 2 / 3 , d ) 1 / 5 , e ) 2 / 7",
"output": [
"b"
]
},
{
"id": "task1424-5869ac1bc7844b258b5af0f19b43929f",
"input": "Problem: a bag contains 3 blue and 5 white marbles . one by one , marbles are drawn out randomly until only two are left in the bag . what is the probability x that out of the two , one is white and one is blue ? \nOptions: a ) 15 / 56 , b ) 41 / 56 , c ) 13 / 28 , d ) 15 / 28 , e ) 5 / 14",
"output": [
"d"
]
},
{
"id": "task1424-24a6cd91914540f19ae5acb0baedd1a1",
"input": "Problem: if a card is drawn from a well shuffled pack of cards , the probability of drawing a spade or a king is ? \nOptions: a ) 4 / 15 , b ) 4 / 10 , c ) 4 / 18 , d ) 4 / 13 , e ) 4 / 11",
"output": [
"d"
]
},
{
"id": "task1424-b2bc6b838591497a8fb5ba8cffdcf029",
"input": "Problem: if a certain coin is flipped , the probability that the coin will land heads is 1 / 2 . if the coin is flipped 5 times , what is the probability that it will land heads up on the first 2 flips but not on the last 3 flips ? \nOptions: a ) 1 / 2 , b ) 1 / 4 , c ) 1 / 8 , d ) 1 / 16 , e ) 1 / 32",
"output": [
"e"
]
},
{
"id": "task1424-039e73d32b0747688034655f0fd1576c",
"input": "Problem: a number is selected at random from the first 40 natural numbers . what is the probability that the number is a multiple of either 2 or 21 ? \nOptions: a ) 21 / 40 , b ) 2 / 5 , c ) 7 / 15 , d ) 4 / 15 , e ) 11 / 30",
"output": [
"a"
]
},
{
"id": "task1424-7a9460439ee54f20a41c663dcbd58082",
"input": "Problem: a number is selected at random from the first 30 natural numbers . what is the probability that the number is a multiple of either 2 or 19 ? \nOptions: a ) 17 / 30 , b ) 2 / 5 , c ) 7 / 15 , d ) 8 / 15 , e ) 11 / 30",
"output": [
"d"
]
},
{
"id": "task1424-d9532e1f18aa4f6f9205ab3c39e03a6e",
"input": "Problem: there are 13 boys and 10 girls in a class . if three students are selected at random , in how many ways that 1 girl or 2 boys are selected ? \nOptions: a ) 88 , b ) 90 , c ) 92 , d ) 96 , e ) 98",
"output": [
"a"
]
},
{
"id": "task1424-9d57cb1fb6bb4ca6a038bfc8bc9f294e",
"input": "Problem: from a group of 3 boys and 3 girls , 2 children are to be randomly selected . what is the probability that 1 boy and 1 girl will be selected ? \nOptions: a ) 1 / 10 , b ) 4 / 9 , c ) 1 / 2 , d ) 9 / 15 , e ) 2 / 3",
"output": [
"d"
]
},
{
"id": "task1424-474abf47c60046be82f5482d657b1188",
"input": "Problem: a basket contains 10 apples , of which 1 is spoiled and the rest are good . if we select 2 apples from the basket simultaneously and at random , what is the probability that the 2 apples selected will include the spoiled apple ? \nOptions: a ) 2 / 9 , b ) 3 / 8 , c ) 2 / 7 , d ) 1 / 6 , e ) 1 / 5",
"output": [
"e"
]
},
{
"id": "task1424-db68672aabfc4a3d88301dfaf464a249",
"input": "Problem: a store has 10 bottles of juice , including 6 bottles of apple juice . in the evening , 6 bottles of juice are sold one by one . what is the probability of selling 2 bottles of apple juice among the 6 bottles ? assume that every bottle has an equal chance of being bought . \nOptions: a ) 1 / 7 , b ) 1 / 12 , c ) 1 / 14 , d ) 1 / 18 , e ) 1 / 21",
"output": [
"c"
]
},
{
"id": "task1424-393c55a1eac148fea622ff8c6ecee499",
"input": "Problem: jane and thomas are among the 8 people from which a committee of 4 people is to be selected . how many different possible committees of 4 people can be selected from these 8 people if at least one of either jane or thomas is to be selected ? \nOptions: a ) 28 , b ) 46 , c ) 55 , d ) 63 , e ) 70",
"output": [
"c"
]
},
{
"id": "task1424-985180afa1974fd8a9f0caad8782ab91",
"input": "Problem: a bag contains 3 blue and 5 white marbles . one by one , marbles are drawn out randomly until only two are left in the bag . what is the probability that out of the two , one is white and one is blue ? \nOptions: a ) 15 / 56 , b ) 41 / 56 , c ) 13 / 28 , d ) 15 / 28 , e ) 5 / 14",
"output": [
"d"
]
},
{
"id": "task1424-60cfd5b4b34a4934ac79e5f54c080652",
"input": "Problem: there are 25 balls in a jar . you take out 5 blue balls without putting them back inside , and now the probability of pulling out a blue ball is 1 / 5 . how many blue balls were there in the beginning ? \nOptions: a ) 12 . , b ) 9 . , c ) 8 . , d ) 7 . , e ) 6 .",
"output": [
"b"
]
},
{
"id": "task1424-b61c84bdf29447f8a71364b46fc9fd50",
"input": "Problem: a meeting has to be conducted with 6 managers . find the number of ways in which the managers may be selected from among 9 managers , if there are 2 managers who refuse to attend the meeting together . \nOptions: a ) 36 , b ) 40 , c ) 42 , d ) 45 , e ) 49",
"output": [
"e"
]
},
{
"id": "task1424-17baf0b3109441eabdc2ca24031fc2f4",
"input": "Problem: a card is drawn from a pack of 52 cards . the probability of not getting a face card ? \nOptions: a ) 9 / 13 , b ) 5 / 12 , c ) 3 / 13 , d ) 6 / 17 , e ) 1 / 13",
"output": [
"a"
]
},
{
"id": "task1424-ce48e4be54df4ec1945eec0f92e3f28a",
"input": "Problem: in a single throw of a die , what is the probability of getting a number greater than 2 ? \nOptions: a ) 1 / 2 , b ) 2 / 5 , c ) 1 / 3 , d ) 2 / 7 , e ) 2 / 3",
"output": [
"e"
]
},
{
"id": "task1424-bbce9766ca804c218df948f5259d5288",
"input": "Problem: a bag contains 3 blue and 5 white marbles . one by one , marbles are drawn out randomly until only two are left in the bag . what is the probability z that out of the two , one is white and one is blue ? \nOptions: a ) 15 / 56 , b ) 41 / 56 , c ) 13 / 28 , d ) 15 / 28 , e ) 5 / 14",
"output": [
"d"
]
},
{
"id": "task1424-6025ebe5a4a6443c8cb44d287c2b4798",
"input": "Problem: 4 dices are thrown at the same time . what is the probability of getting only 2 dices showing the same face ? \nOptions: a ) 4 / 9 , b ) 5 / 9 , c ) 11 / 18 , d ) 7 / 9 , e ) none of the above",
"output": [
"b"
]
},
{
"id": "task1424-750262b24c604073b72c70f7c317974f",
"input": "Problem: x , y , and z are all unique numbers . if x is chosen randomly from the set { 5 , 6 , 7 , 8 , 9 , 10 , 11 } and y and z are chosen randomly from the set { 20 , 21 , 22 , 23 } , what is the probability that x and y are prime and z is not ? \nOptions: a ) 1 / 5 , b ) 3 / 20 , c ) 1 / 7 , d ) 2 / 15 , e ) 3 / 28",
"output": [
"e"
]
},
{
"id": "task1424-550ccc0bfde743b5bc5a15536b35e0b7",
"input": "Problem: a meeting has to be conducted with 4 managers . find the number of ways in which the managers may be selected from among 8 managers , if there are 2 managers who refuse to attend the meeting together . \nOptions: a ) 48 , b ) 55 , c ) 58 , d ) 62 , e ) 70",
"output": [
"b"
]
},
{
"id": "task1424-4d64f36f5fc643dd80f65fd648acc5de",
"input": "Problem: the membership of a committee consists of 3 english teachers , 4 mathematics teachers , and 2 social studies teachers . if 2 committee members are to be selected at random to write the committee ’ s report , what is the probability that the two members selected will both be english teachers ? \nOptions: a ) 2 / 3 , b ) 1 / 3 , c ) 2 / 9 , d ) 1 / 12 , e ) 1 / 24",
"output": [
"d"
]
},
{
"id": "task1424-26cab6d49e2e439a8cfb4a4a49913dd1",
"input": "Problem: into a bag there are 20 honey and 5 cherry candies . if a boy pick only two candies simultaneous and randomly , what is the probability that he picks one candy of each flavor ? \nOptions: a ) 2 / 25 , b ) 1 / 50 , c ) 1 / 12 , d ) 1 / 6 , e ) 1 / 3",
"output": [
"e"
]
},
{
"id": "task1424-16b4cfbc03de49a38dee592f5e549a65",
"input": "Problem: what is the probability of getting a number less than 4 when a die is rolled ? \nOptions: a ) 5 / 5 , b ) 1 / 2 , c ) 5 / 1 , d ) 5 / 7 , e ) 5 / 2",
"output": [
"b"
]
},
{
"id": "task1424-efe1a145de6f48c6adbee2871959d7b5",
"input": "Problem: what is the probability of randomly selecting one of the shortest diagonals from all the diagonals of a regular octagon ? \nOptions: a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 5 , e ) 7 / 8",
"output": [
"d"
]
},
{
"id": "task1424-850098ecda9045c398b324ad6311f7be",
"input": "Problem: what is the probability q of randomly selecting an arrangement of the letters of the wordmediterraneanin which the first letter is e and the last letter is r ? \nOptions: a ) 1 / 13 , b ) 1 / 20 , c ) 1 / 26 , d ) 1 / 50 , e ) 1 / 100",
"output": [
"c"
]
},
{
"id": "task1424-a30b1999522f49d5875181c97833e04d",
"input": "Problem: denise is trying to open a safe whose combination she does not know . if the safe has 4000 possible combinations , and she can try 75 different possibilities , what is the probability that she does not pick the one correct combination . \nOptions: a ) 1 , b ) 159 / 160 , c ) 157 / 160 , d ) 4 3 / 160 , e ) 0",
"output": [
"c"
]
},
{
"id": "task1424-c686c6569176466e89f3f667fb88a07b",
"input": "Problem: if two dice are thrown together , the probability of getting an even prime number on the dice is \nOptions: a ) 1 / 36 , b ) 1 / 18 , c ) 1 / 13 , d ) 1 / 9 , e ) 5 / 36",
"output": [
"a"
]
},
{
"id": "task1424-3346dd99fb564bd7b662b13a564c3122",
"input": "Problem: the only items of clothing at michelle ’ s boutique are 4 shirts , 8 pairs of pants and 18 ties . what is the probability of randomly selecting 2 ties out of all the items in michelle ’ s boutique ? \nOptions: a ) 51 / 145 , b ) 9 / 25 , c ) 3 / 5 , d ) 94 / 145 , e ) 5 / 6",
"output": [
"a"
]
},
{
"id": "task1424-62186260435d4ca4a84937500c420fa0",
"input": "Problem: what is the probability of getting sum 10 with the help of three dice ? \nOptions: a ) 1 / 4 , b ) 1 / 8 , c ) 1 / 16 , d ) 1 / 24 , e ) 1 / 32",
"output": [
"b"
]
},
{
"id": "task1424-314bc00b3be94640b3c35960a2b4542c",
"input": "Problem: in a garden , there are yellow and green flowers which are straight and curved . if the probability of picking a green flower is 2 / 3 and picking a straight flower is 1 / 2 , then what is the probability of picking a flower which is yellow and straight \nOptions: a ) 1 / 6 , b ) 1 / 8 , c ) 1 / 4 , d ) 3 / 4 , e ) 7 / 8",
"output": [
"a"
]
},
{
"id": "task1424-a15c4fea78444210a1103628f6529038",
"input": "Problem: three unbiased coins are tossed , what is the probability of getting at least 2 tails ? \nOptions: a ) 1 / 5 , b ) 1 / 7 , c ) 1 / 8 , d ) 1 / 2 , e ) 1 / 10",
"output": [
"d"
]
},
{
"id": "task1424-ca3aa032b2bf4536801c2573ec6b4c3e",
"input": "Problem: how many positive integers less than 600 can be formed using the numbers 1 , 2 , 3 , 5 and 6 for the digits ? \nOptions: a ) 48 , b ) 130 , c ) 66 , d ) 68 , e ) 84",
"output": [
"b"
]
},
{
"id": "task1424-2ddd996aea8d45819925ec8bedb684b0",
"input": "Problem: if a certain coin is flipped , the probability that the coin will land heads is 1 / 2 . if the coin is flipped 6 times , what is the probability that it will land heads up on the first 4 flips but not on the last 2 flips ? \nOptions: a ) 1 / 8 , b ) 1 / 16 , c ) 1 / 32 , d ) 1 / 64 , e ) 1 / 128",
"output": [
"d"
]
},
{
"id": "task1424-a8c080e1f691440b8d5a2122f0e48a97",
"input": "Problem: there are two bags a and b . a contains 6 red flowers and 3 pink flowers . where as bag b contains 2 red flowers and 7 pink flowers . one flower is chosen from a bag randomly . what is the probability that the flower chosen is pink ? \nOptions: a ) 5 / 8 , b ) 5 / 6 , c ) 5 / 1 , d ) 5 / 9 , e ) 5 / 2",
"output": [
"d"
]
},
{
"id": "task1424-07d735a2ca184e90b3e350c8a0450d5d",
"input": "Problem: there are 23 students in a class . in how many different ways can a committee of 3 students be formed ? \nOptions: a ) 1254 , b ) 1482 , c ) 1771 , d ) 1875 , e ) 1923",
"output": [
"c"
]
},
{
"id": "task1424-b1f8a385c98348348466948c8ee8c06b",
"input": "Problem: wink , inc . follows a certain procedure that requires two tasks to be finished independently in order for a job to be done . on any given day , there is a 7 / 8 probability that task 1 will be completed on time , and a 1 / 5 probability that task 2 will be completed on time . on a certain day , what is the probability that task 1 will be completed on time , but task 2 will not ? \nOptions: a ) 1 / 20 , b ) 3 / 40 , c ) 13 / 40 , d ) 7 / 10 , e ) 13 / 22",
"output": [
"d"
]
},
{
"id": "task1424-25b2a60a6e20489fa3ceca66f981ae6b",
"input": "Problem: in a bag containing 3 balls , a white ball was placed and then 1 ball was taken out at random . what is theprobability that the extracted ball would turn onto be white , if all possible hypothesisconcerning the color of the balls that initially in the bag were equally possible ? \nOptions: a ) 3 / 5 , b ) 5 / 8 , c ) 6 / 7 , d ) 7 / 8 , e ) 6 / 7",
"output": [
"b"
]
},
{
"id": "task1424-bd2735949ca643f6979219e93991c3b8",
"input": "Problem: if a certain coin is flipped , the probability that the coin will land heads is 1 / 2 . if the coin is flipped 5 times , what is the probability that it will land heads up on the first 4 flips but not on the last flip ? \nOptions: a ) 1 / 2 , b ) 1 / 4 , c ) 1 / 8 , d ) 1 / 16 , e ) 1 / 32",
"output": [
"e"
]
},
{
"id": "task1424-30c3dbf32b924735b73b533bf29a336d",
"input": "Problem: if 4 people are selected from a group of 5 married couples , what is the probability that none of them would be married to each other ? \nOptions: a ) 1 / 33 , b ) 2 / 33 , c ) 1 / 3 , d ) 16 / 33 , e ) 8 / 21",
"output": [
"e"
]
},
{
"id": "task1424-5919c733623c489faa570b0620111441",
"input": "Problem: a circular dartboard of radius 1 foot is at a distance of 20 feet from you . you throw a dart at it and it hits the dartboard at some point q in the circle . what is the probability that q is closer to the center of the circle than the periphery ? \nOptions: a ) 0.75 , b ) 1 , c ) 0.25 , d ) 0.5 , e ) 0.58",
"output": [
"c"
]
},
{
"id": "task1424-6c1110b9d5da4ab4a3e64c83d35a7e54",
"input": "Problem: the maitre ' d at an expensive manhattan restaurant has noticed that 60 % of the couples order dessert and coffee . however , 20 % of the couples who order dessert do n ' t order coffee . what is the probability r that the next couple the maitre ' d seats will not order dessert ? \nOptions: a ) 20 % , b ) 25 % , c ) 40 % , d ) 60 % , e ) 75 %",
"output": [
"b"
]
},
{
"id": "task1424-70d0aff9603447d581d206dc2d9cf9b1",
"input": "Problem: three 8 faced dice are thrown together . the probability that all the three show the same number on them is ? \nOptions: a ) 1 / 38 , b ) 1 / 48 , c ) 1 / 56 , d ) 1 / 64 , e ) 1 / 68",
"output": [
"d"
]
},
{
"id": "task1424-745310e8baf24de3966ab5d0e810c707",
"input": "Problem: find the probability that a number selected from numbers 1 , 2 , 3 , . . . , 45 is a prime number , when each of the given numbers is equally likely to be selected ? \nOptions: a ) 10 / 45 , b ) 14 / 45 , c ) 8 / 45 , d ) 3 / 45 , e ) 7 / 45",
"output": [
"b"
]
},
{
"id": "task1424-7d9c6d62b8c2490d8cf54f0f32a19318",
"input": "Problem: kim has 9 pairs of shoes ; each pair is a different color . if kim randomly selects 2 shoes without replacement from the 18 shoes , what is the probability that she will select 2 shoes of the same color ? \nOptions: a ) 2 / 5 , b ) 11 / 5 , c ) 1 / 9 , d ) 1 / 17 , e ) 1 / 5",
"output": [
"d"
]
},
{
"id": "task1424-98507d97613c416eaafeb56cb24e4835",
"input": "Problem: the chance of rain on any given day in tel - aviv is 50 % . what is the probability e that it rained in tel - aviv on exactly 4 out of 6 randomly chosen days ? \nOptions: a ) 15 / 64 , b ) 30 / 64 , c ) 1 / 2 , d ) 1 / 4 , e ) 52 / 64",
"output": [
"a"
]
},
{
"id": "task1424-311f571b01e64454b6d01d17661e4564",
"input": "Problem: find the probability that a number selected from numbers 1 , 2 , 3 , . . . , 35 is a prime number , when each of the given numbers is equally likely to be selected ? \nOptions: a ) 10 / 35 , b ) 11 / 35 , c ) 8 / 35 , d ) 3 / 35 , e ) 7 / 35",
"output": [
"b"
]
},
{
"id": "task1424-06789966931e45a4957dda7782d9ff8a",
"input": "Problem: a fair coin is tossed 15 times . what is the probability of getting more heads than tails in 15 tosses ? \nOptions: a ) 1 / 2 , b ) 63 / 128 , c ) 4 / 7 , d ) 61 / 256 , e ) 63 / 64",
"output": [
"a"
]
},
{
"id": "task1424-cab545c10bbb40a1b6171ba7e49c39a2",
"input": "Problem: kim has 7 pairs of shoes ; each pair is a different color . if kim randomly selects 2 shoes without replacement from the 14 shoes , what is the probability that she will select 2 shoes of the same color ? \nOptions: a ) 1 / 13 , b ) 1 / 15 , c ) 11 / 9 , d ) 1 / 10 , e ) 1 / 25",
"output": [
"a"
]
},
{
"id": "task1424-3364d93158db44b5b74928469bd46e8f",
"input": "Problem: a jar contains only red , yellow , and orange marbles . if there are 1 red , 5 yellow , and 4 orange marbles , and 3 marbles are chosen from the jar at random without replacing any of them , what is the probability that 2 yellow , 1 red , and no orange marbles will be chosen ? \nOptions: a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 5 / 22",
"output": [
"b"
]
},
{
"id": "task1424-83389fa5d1b44fd482660ab82435f13c",
"input": "Problem: a certain junior class has 1000 students and a certain senior class has 900 students . among these students , there are 60 siblings pairs each consisting of 1 junior and 1 senior . if 1 student is to be selected at random from each class , what is the probability that the 2 students selected will be a sibling pair ? \nOptions: a ) 3 / 40000 , b ) 2 / 30000 , c ) 9 / 2000 , d ) 1 / 60 , e ) 1 / 15",
"output": [
"b"
]
},
{
"id": "task1424-80e9a8df1cea48388351ea5b7b3d9bfb",
"input": "Problem: three unbiased coins are tossed . what is the probability of getting at least 2 heads ? \nOptions: a ) 1 / 4 , b ) 1 / 2 , c ) 1 / 3 , d ) 1 / 8 , e ) 1 / 6",
"output": [
"b"
]
},
{
"id": "task1424-131adafc16ef420193d2841cdd5b629e",
"input": "Problem: there are 4 red shoes & 4 green shoes . if two of red shoes are drawn what is the probability of getting red shoes \nOptions: a ) 1 / 3 , b ) 1 / 14 , c ) 3 / 14 , d ) 1 / 15 , e ) 1 / 16",
"output": [
"c"
]
},
{
"id": "task1424-a5df8d63891b4a5ba0f80ce55abd6a6c",
"input": "Problem: how many positive integers less than 500 can be formed using the numbers 1 , 2,3 , and 5 for digits , each digit being used only once . \nOptions: a ) 34 , b ) 677 , c ) 197 , d ) 177 , e ) 191",
"output": [
"a"
]
},
{
"id": "task1424-25a04132901c4b6897fabfc751be8774",
"input": "Problem: when two dice are rolled , what is the probability that the sum of the two numbers is 6 ? \nOptions: a ) 1 / 9 , b ) 5 / 36 , c ) 1 / 3 , d ) 2 / 36 , e ) none of the above",
"output": [
"b"
]
},
{
"id": "task1424-e7059afc09334312aaa81a1cb0fe5229",
"input": "Problem: three unbiased coins are tossed . what is the probability of getting 1 heads , 1 tail ? \nOptions: a ) 3 / 4 , b ) 1 / 4 , c ) 3 / 8 , d ) 7 / 8 , e ) 2 / 8",
"output": [
"e"
]
},
{
"id": "task1424-d296962359ef48309345ba67265e0da8",
"input": "Problem: a card is drawn from a pack of 52 cards . the probability of ge ƫ ng a queen of club or a king of heart is \nOptions: a ) 1 / 13 , b ) 2 / 13 , c ) 1 / 26 , d ) 1 / 52 , e ) none of these",
"output": [
"c"
]
},
{
"id": "task1424-ff899c35c52f426ca1b8189791080d54",
"input": "Problem: a meeting has to be conducted with 4 managers . find the number of ways in which the managers may be selected from among 7 managers , if there are 2 managers who refuse to attend the meeting together . \nOptions: a ) 18 , b ) 21 , c ) 25 , d ) 30 , e ) 35",
"output": [
"c"
]
},
{
"id": "task1424-5dc796ebcfe04868b2020b59cff86b25",
"input": "Problem: when two dice are rolled , what is the probability that the sum is either 7 or 11 ? \nOptions: a ) 1 / 4 , b ) 1 / 9 , c ) 4 / 3 , d ) 3 / 9 , e ) 2 / 9",
"output": [
"e"
]
},
{
"id": "task1424-340b3b7a5f8b4e24a766675040b34495",
"input": "Problem: from a pack of cards , two cards are drawn one after the other , with replacement . what is the probability that the first card is a club and the second card is a king ? \nOptions: a ) 2 / 13 , b ) 1 / 26 , c ) 5 / 26 , d ) 1 / 52 , e ) 17 / 52",
"output": [
"d"
]
},
{
"id": "task1424-d68bcf8e22664fe1a281bfae5dabcc9b",
"input": "Problem: a basket contains 6 apples , of which 1 is spoiled and the rest are good . if we select 2 apples from the basket simultaneously and at random , what is the probability that the 2 apples selected will include the spoiled apple ? \nOptions: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 5 , e ) 1 / 6",
"output": [
"a"
]
},
{
"id": "task1424-f20018b3b03343cb961ee32656dfee10",
"input": "Problem: an urn contains 5 red , 6 blue and 8 green balls . 4 balls are randomly selected from the urn , find the probability that the drawn ball are 1 blue and 3 red ? \nOptions: a ) 1 / 969 , b ) 2 / 969 , c ) 4 / 969 , d ) 5 / 323 , e ) 21 / 789",
"output": [
"d"
]
},
{
"id": "task1424-50c499c8d2e24c67a7e0a42aeb952867",
"input": "Problem: what is the probability of getting a sum 9 from two throws of dice \nOptions: a ) 1 / 3 , b ) 1 / 9 , c ) 1 / 12 , d ) 2 / 9 , e ) none of these",
"output": [
"b"
]
},
{
"id": "task1424-ead20b72e27947eea656ddf1f608d130",
"input": "Problem: two unbiased coins are tossed . find the probability of getting at most one head ? \nOptions: a ) 1 / 2 , b ) 3 / 4 , c ) 2 / 5 , d ) 2 / 3 , e ) 1 / 4",
"output": [
"b"
]
},
{
"id": "task1424-23244a1d8d334c46b3db66b88b462245",
"input": "Problem: a bag contains 6 black and 6 white balls . one ball is drawn at random . what is the probability that the ball drawn is white ? \nOptions: a ) 3 / 4 , b ) 1 / 2 , c ) 1 / 7 , d ) 1 / 8 , e ) 4 / 3",
"output": [
"b"
]
},
{
"id": "task1424-0e64d0a508cf49f4a5b93fc23d5ab5cf",
"input": "Problem: the membership of a committee consists of 3 english teachers , 4 mathematics teachers , and 2 social studies teachers . if 2 committee members are to be selected at random to write the committee ’ s report , what is the probability that the two members selected will both be social teachers ? \nOptions: a ) 2 / 3 , b ) 1 / 12 , c ) 2 / 9 , d ) 1 / 2 , e ) 1 / 24",
"output": [
"b"
]
},
{
"id": "task1424-8b9b8c4128af467084b265dcdda8c16a",
"input": "Problem: what is the probability of randomly selecting one of the shortest diagonals from all the diagonals of a regular hexagon ? \nOptions: a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 7 / 9",
"output": [
"d"
]
},
{
"id": "task1424-9928748d00bb4af99c04b3b9a1ad8c4c",
"input": "Problem: a meeting has to be conducted with 5 managers . find the number of ways in which the managers be selected from among 9 managers , if 2 managers will not attend the meeting together ? \nOptions: a ) 35 , b ) 91 , c ) 120 , d ) 126 , e ) 150",
"output": [
"b"
]
},
{
"id": "task1424-95fbc6c1a0424ffb887e25930667f118",
"input": "Problem: the membership of a committee consists of 3 english teachers , 4 mathematics teachers , and 3 social studies teachers . if 2 committee members are to be selected at random to write the committee ’ s report , what is the probability that the two members selected will both be english teachers ? \nOptions: a ) 2 / 3 , b ) 1 / 3 , c ) 2 / 9 , d ) 1 / 12 , e ) 1 / 24",
"output": [
"d"
]
},
{
"id": "task1424-dce4b1c210eb4a6ba5cf992ce58ad833",
"input": "Problem: in a certain animal population , for each of the first 3 months of life , the probability that an animal will die during that month is 1 / 10 . for a group of 300 newborn members of the population , approximately how many would be expected to survive the first 3 months of life ? \nOptions: a ) 219 , b ) 246 , c ) 252 , d ) 262 , e ) 270",
"output": [
"a"
]
},
{
"id": "task1424-8ddffc97ff4a4046b7d697a76c55203a",
"input": "Problem: a card is drawn from a pack of 52 cards . the probability of getting a queen of club or a king of heart is : \nOptions: a ) 1 / 26 , b ) 1 / 52 , c ) 2 / 62 , d ) 2 / 26 , e ) 3 / 26",
"output": [
"a"
]
},
{
"id": "task1424-34850bcb02a74ebea27f3d61e75e225f",
"input": "Problem: a certain junior class has 1,000 students and a certain senior class has 600 students . among these students , there are 60 siblings pairs , each consisting of 1 junior and 1 senior . if 1 student is to be selected at random from each class , what is the probability that the 2 students selected at will be a sibling pair ? \nOptions: a ) 3 / 40,000 , b ) 1 / 10,000 , c ) 9 / 2,000 , d ) 1 / 60 , e ) 1 / 15",
"output": [
"b"
]
},
{
"id": "task1424-e18e18c040ad492ba68103b7f7d4544b",
"input": "Problem: the chance of rain on any given day in tel - aviv is 50 % . what is the probability w that it rained in tel - aviv on exactly 4 out of 6 randomly chosen days ? \nOptions: a ) 15 / 64 , b ) 30 / 64 , c ) 1 / 2 , d ) 1 / 4 , e ) 52 / 64",
"output": [
"a"
]
},
{
"id": "task1424-69b9b9521f6c47b98331dcf0884c7cd0",
"input": "Problem: a bag contains 10 red jellybeans and 10 blue jellybeans . if 3 jellybeans are removed one at a time , at random and are not replaced , what is the probability e that all 3 jellybeans removed from the bag are blue ? \nOptions: a ) 9 / 100 , b ) 2 / 19 , c ) 1 / 8 , d ) 3 / 20 , e ) 3 / 10",
"output": [
"b"
]
},
{
"id": "task1424-ec891bbbccad4730a3c8624e223f6639",
"input": "Problem: in how many ways 4 boys and 4 girls can be seated in a row so that they are alternate . \nOptions: a ) 144 , b ) 288 , c ) 12 , d ) 576 , e ) none",
"output": [
"d"
]
},
{
"id": "task1424-47e0734f21984d6fb2230ebc2b3e17d9",
"input": "Problem: a bag consists of 20 marbles , of which 6 are blue , 9 are red , and the remainder are white . if lisa is to select a marble from the bag at random , what is the probability that the marble will be red or white ? \nOptions: a ) 7 / 10 , b ) 2 / 4 , c ) 1 / 4 , d ) 1 / 8 , e ) 1 / 16",
"output": [
"a"
]
},
{
"id": "task1424-16452819f7e148a4abec9c60042d8292",
"input": "Problem: in a certain animal population , for each of the first 3 months of life , the probability that an animal will die during that month is 1 / 4 . for a group of 200 newborn members of the population , approximately how many would be expected to survive the first 3 months of life ? \nOptions: a ) 40 , b ) 46 , c ) 52 , d ) 62 , e ) 85",
"output": [
"e"
]
},
{
"id": "task1424-0ef176989ea1452e837efbe4598681ab",
"input": "Problem: in a certain animal population , for each of the first 3 months of life , the probability that an animal will die during that month is 1 / 10 . for a group of 500 newborn members of the population , approximately how many would be expected to survive the first 3 months of life ? \nOptions: a ) 340 , b ) 346 , c ) 352 , d ) 365 , e ) 370",
"output": [
"d"
]
},
{
"id": "task1424-41f18241975e4553942e9a90d08d2014",
"input": "Problem: if a card is drawn from a well shuffled pack of cards , the probability of drawing a spade or a king is - . \nOptions: a ) 2 / 10 , b ) 4 / 13 , c ) 3 / 5 , d ) 9 / 7 , e ) 1 / 4",
"output": [
"b"
]
},
{
"id": "task1424-2075ff58f084486c829d29cbce400493",
"input": "Problem: a multiple choice test consists of 4 questions , and each question has 5 answer choices . in how many ways can the test be completed if every question is unanswered ? \nOptions: a ) 24 , b ) 120 , c ) 625 , d ) 720 , e ) 1024",
"output": [
"c"
]
},
{
"id": "task1424-a09fb761283b4382b91f1da2a754a2cb",
"input": "Problem: from a group of 4 boys and 4 girls , 2 children are to be randomly selected . what is the probability that 1 boy and 1 girl will be selected ? \nOptions: a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 5 , d ) 4 / 7 , e ) 5 / 9",
"output": [
"d"
]
},
{
"id": "task1424-9ea16c869921456d80b5bb8df528ff76",
"input": "Problem: rhonda picked 2 pen from the table , if there were 7 pens on the table and 5 belongs to jill , what is the probability that the 2 pen she picked does not belong to jill ? . \nOptions: a ) 5 / 42 , b ) 2 / 42 , c ) 7 / 42 , d ) 2 / 7 , e ) 5 / 7",
"output": [
"b"
]
},
{
"id": "task1424-55f5a1e0867c4f5181232cf32a4f3b85",
"input": "Problem: what is the probability that carol and bernie will get selected for a job they both applied for in a company , given that their chances of getting selected is 4 / 5 and 3 / 5 respectively ? \nOptions: a ) 8 / 25 , b ) 11 / 24 , c ) 12 / 25 , d ) 12 / 25 , e ) 12 / 23",
"output": [
"d"
]
},
{
"id": "task1424-a4dc71c220f947b2923b0262418ee503",
"input": "Problem: the set s consists of 5 numbers : { 1 , 2,3 , 4,5 } . if all possible subsets including the null set are created and one subset is chosen at random , what is the probability that the subset has 4 or 5 as its largest number ? \nOptions: a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 4 , d ) 5 / 8 , e ) 11 / 16",
"output": [
"c"
]
},
{
"id": "task1424-694b4453ae7e419caa54dfcfa1e90df3",
"input": "Problem: four dice are thrown simultaneously . find the probability that all of them show the same face . \nOptions: a ) 1 / 216 , b ) 1 / 215 , c ) 5 / 300 , d ) 1 / 415 , e ) 1 / 500",
"output": [
"a"
]
},
{
"id": "task1424-15100b304d3c4764bf35b126ce317126",
"input": "Problem: a basket contains 8 apples , of which 1 is spoiled and the rest are good . if we select 2 apples from the basket simultaneously and at random , what is the probability that the 2 apples selected will include the spoiled apple ? \nOptions: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 5 , e ) 1 / 6",
"output": [
"c"
]
},
{
"id": "task1424-bd33413536514522ad45f74dec210528",
"input": "Problem: what is the probability that when a hand o f 6 cards is drawn from a well shuffled deck of 52 cards , it contains 2 queen ? \nOptions: a ) 1 / 23445 , b ) 113 / 22434 , c ) 29187 by 1017926 , d ) 1017926 / 29187 , e ) none of these",
"output": [
"c"
]
},
{
"id": "task1424-7ab213a7745a47b0b7ff80e428185e06",
"input": "Problem: if a coin has an equal probability of landing heads up or tails up each time it is flipped , what is the probability that the coin will land heads up exactly once in 3 consecutive flips ? \nOptions: a ) 0.125 , b ) 0.25 , c ) 0.75 , d ) 0.375 , e ) 0.666",
"output": [
"d"
]
},
{
"id": "task1424-3ccf80d9d25a478cb0166bdc8b2452b4",
"input": "Problem: two dice are thrown simultaneously . what is the probability of getting two numbers whose product is even ? \nOptions: a ) 1 / 2 , b ) 3 / 8 , c ) 3 / 4 , d ) 5 / 16 , e ) 9 / 16",
"output": [
"c"
]
},
{
"id": "task1424-670959a0850f4a958b637d87d8239cff",
"input": "Problem: a bag contains 3 red , 5 yellow and 4 green balls . 3 balls are drawn randomly . what is the probability that the balls drawn contain balls of different colours ? \nOptions: a ) 2 / 7 , b ) 3 / 5 , c ) 3 / 11 , d ) 1 / 4 , e ) 7 / 16",
"output": [
"c"
]
},
{
"id": "task1424-61f99b4063ae4dffbafed4d1d1093590",
"input": "Problem: there is a 30 % chance that tigers will not win at all during the whole season . there is a 30 % chance that portugeese will not play at all in the whole season . what is the greatest possible probability that the tigers will win and portugeese will play during the season ? \nOptions: a ) 55 % , b ) 60 % , c ) 70 % , d ) 72 % , e ) 80 %",
"output": [
"c"
]
},
{
"id": "task1424-ea9dd124cb9f464ba87593c592d2cabb",
"input": "Problem: what is the probability of drawn an ace or a space or both from a dew of cards . \nOptions: a ) 14 / 52 , b ) 15 / 52 , c ) 16 / 52 , d ) 17 / 52 , e ) 18 / 52",
"output": [
"c"
]
},
{
"id": "task1424-048d286b62574c2897438e924f505c4c",
"input": "Problem: a box contains 3 red balls and 3 black balls . one by one , every ball is selected at random without replacement . what is the probability that the fourth ball selected is black ? \nOptions: a ) 1 / 4 , b ) 1 / 2 , c ) 1 / 2 , d ) 2 , e ) 2 / 3",
"output": [
"d"
]
},
{
"id": "task1424-c010371ab34b44ccbbf000002d6b9e4e",
"input": "Problem: a bag contains 3 blue and 5 white marbles . one by one , marbles are drawn out randomly until only two are left in the bag . what is the probability c that out of the two , one is white and one is blue ? \nOptions: a ) 15 / 56 , b ) 41 / 56 , c ) 13 / 28 , d ) 15 / 28 , e ) 5 / 14",
"output": [
"d"
]
},
{
"id": "task1424-6a85ad01964f423a9129242283b34618",
"input": "Problem: two cards are drawn together from a pack of 52 cards . the probability that one is a club and other is a diamond , is : \nOptions: a ) 29 / 34 , b ) 47 / 100 , c ) 3 / 20 , d ) 13 / 102 , e ) none of these",
"output": [
"d"
]
},
{
"id": "task1424-8ff736f050044953b310ef9c09087f1e",
"input": "Problem: a string of 30 light bulbs is wired in such a way that if any individual light bulb fails , the entire string fails . if for each individual light bulb the probability of failing during time period t is 0.1 , what is the probability that the string of light bulbs will fail during the time period t ? \nOptions: a ) 0.1 , b ) ( 0.1 ) ^ 30 , c ) 1 - ( 0.1 ) ^ 30 , d ) ( 0.93 ) ^ 30 , e ) 1 - ( 0.90 ) ^ 30",
"output": [
"e"
]
},
{
"id": "task1424-d203edcf4f4e4879b3e576d851493df8",
"input": "Problem: the chance of rain on any given day in tel - aviv is 50 % . what is the probability a that it rained in tel - aviv on exactly 4 out of 6 randomly chosen days ? \nOptions: a ) 15 / 64 , b ) 30 / 64 , c ) 1 / 2 , d ) 1 / 4 , e ) 52 / 64",
"output": [
"a"
]
},
{
"id": "task1424-f6df76ed596d4de58b373a03421733f8",
"input": "Problem: a box contains 10 black , 5 red and 4 green marbles . 3 marbles are drawn from the box at random . what is the probability that all the three marbles are of the same color ? \nOptions: a ) 143 / 969 , b ) 134 / 969 , c ) 120 / 969 , d ) 19 / 969 , e ) 120 / 134",
"output": [
"b"
]
},
{
"id": "task1424-e57863447453426e8b9d4568cf908ba5",
"input": "Problem: three unbiased coins are tossed . what is the probability of getting 3 heads and 1 tail ? \nOptions: a ) 3 / 4 , b ) 1 / 4 , c ) 3 / 8 , d ) 1 / 2 , e ) 1 / 8",
"output": [
"d"
]
},
{
"id": "task1424-d0e282886ffd425db14ce9953a6a59c2",
"input": "Problem: a jar contains only red , yellow , and orange marbles . if there are 3 red , 7 yellow , and 4 orange marbles , and 3 marbles are chosen from the jar at random without replacing any of them , what is the probability that 2 yellow , 1 red , and no orange marbles will be chosen ? \nOptions: a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 5 / 22",
"output": [
"e"
]
},
{
"id": "task1424-d6c784c7b5be4dcfaa9eb8cb7c030463",
"input": "Problem: on a windy day , out of every 3 sand dunes formed , only 1 remains . out of 5 blown - out sand - dunes , 1 has treasure and only 2 out of 3 sand dunes formed have lucky coupons . find the probability that the blown - out sand dune will contain both the things . \nOptions: a ) 2 / 25 , b ) 4 / 75 , c ) 7 / 75 , d ) 3 / 5 , e ) 4 / 45",
"output": [
"e"
]
},
{
"id": "task1424-413e88b757c64699984aac4f6562aa56",
"input": "Problem: a box contains 100 balls , numbered from 1 to 100 . if 3 balls are selected at random and with replacement from the box . if the 3 numbers on the balls selected contain two odd and one even . what is the probability g that the first ball picked up is odd numbered ? \nOptions: a ) 0 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 1",
"output": [
"d"
]
},
{
"id": "task1424-74410afe1ef84441b2b6364884b286a9",
"input": "Problem: if a certain coin is flipped , the probability that the coin will land heads is 1 / 2 . if the coin is flipped 5 times , what is the probability that it will land heads up on the first 3 flips and not on the last 2 flips ? \nOptions: a ) 3 / 5 , b ) 1 / 2 , c ) 1 / 5 , d ) 1 / 8 , e ) 1 / 32",
"output": [
"e"
]
},
{
"id": "task1424-3f711706fb1e450397a17eefad2d468b",
"input": "Problem: there are 6 red balls and 4 blue balls in a jar . if 3 balls are selected from the jar , what is the probability that all 3 balls selected are red balls ? \nOptions: a ) 1 / 3 , b ) 1 / 6 , c ) 5 / 12 , d ) 5 / 24 , e ) 7 / 24",
"output": [
"b"
]
},
{
"id": "task1424-991368453e1a4a52a0295ab2e0c20d21",
"input": "Problem: four 6 faced dice are thrown together . the probability that all the four show the same number on them is ? \nOptions: a ) 1 / 248 , b ) 1 / 216 , c ) 1 / 144 , d ) 1 / 200 , e ) 1 / 242",
"output": [
"b"
]
},
{
"id": "task1424-8eb4082ca2a34daf8f21a512c3bdccf9",
"input": "Problem: a bag contains 10 red jellybeans and 10 blue jellybeans . if 3 jellybeans are removed one at a time , at random and are not replaced , what is the probability y that all 3 jellybeans removed from the bag are blue ? \nOptions: a ) 9 / 100 , b ) 2 / 19 , c ) 1 / 8 , d ) 3 / 20 , e ) 3 / 10",
"output": [
"b"
]
},
{
"id": "task1424-6f6fca40095f440cb56b3fe30902f76a",
"input": "Problem: a fair coin is tossed 13 times . what is the probability of getting more heads than tails in 13 tosses ? \nOptions: a ) 1 / 2 , b ) 63 / 128 , c ) 4 / 7 , d ) 61 / 256 , e ) 63 / 64",
"output": [
"a"
]
},
{
"id": "task1424-22e31a15453f4c349e3c40342b47b8e8",
"input": "Problem: if a coin has an equal probability of landing heads up or tails up each time it is flipped , what is the probability that the coin will land tails up exactly once in 3 consecutive flips ? \nOptions: a ) 0.125 , b ) 0.375 , c ) 0.325 , d ) 0.5 , e ) 0.666",
"output": [
"b"
]
},
{
"id": "task1424-2257f1850a534e949732047f6b4beee1",
"input": "Problem: a box contains 1 red balls and 5 black balls . one by one , every ball is selected at random without replacement . what is the probability that the fourth ball selected is black ? \nOptions: a ) 1 / 4 , b ) 1 / 2 , c ) 1 / 2 , d ) 5 / 8 , e ) 2 / 3",
"output": [
"c"
]
},
{
"id": "task1424-eec18b3acb184ea1931ddf4368f7a501",
"input": "Problem: a fair coin is tossed 3 times . what is the probability of getting at least 2 tails ? \nOptions: a ) 3 / 4 , b ) 3 / 2 , c ) 1 / 2 , d ) 3 / 4 , e ) 1 / 4",
"output": [
"c"
]
},
{
"id": "task1424-d978331df78f4fcc8a73f2c4eb01cc4d",
"input": "Problem: from a pack of cards , two cards are drawn one after the other , with replacement . what is the probability that the first card is a black card and the second card is a king or queen ? \nOptions: a ) 1 / 52 , b ) 1 / 13 , c ) 1 / 26 , d ) 3 / 26 , e ) 17 / 26",
"output": [
"b"
]
},
{
"id": "task1424-83d608c513e2433896f804571a0ec8da",
"input": "Problem: three 7 faced dice are thrown together . the probability that all the three show the same number on them is ? \nOptions: a ) 1 / 38 , b ) 1 / 49 , c ) 1 / 39 , d ) 1 / 42 , e ) 1 / 29",
"output": [
"b"
]
},
{
"id": "task1424-d81fd6dbf7a848b2adba44a39360b18e",
"input": "Problem: there are 5 pairs of socks and 2 socks are worn from that such that the pair of socks worn are not of the same pair . what is the number of pair that can be formed . \nOptions: a ) 19 , b ) 20 , c ) 30 , d ) 32 , e ) 25",
"output": [
"b"
]
},
{
"id": "task1424-a25001f15f7744578ed35c4d11ad587b",
"input": "Problem: potato chips are on sale , buy 2 get 1 free . there are only 9 bags of chips left ( 4 plain and 5 bbq ) . a shopper randomly grabs 3 bags . what is the probability the shopper will grab exactly 3 bags of bbq chips ? \nOptions: a ) 2 / 3 , b ) 1 / 3 , c ) 1 / 5 , d ) 5 / 42 , e ) 7 / 42",
"output": [
"d"
]
},
{
"id": "task1424-ae0f627f7f354e32bdbcab46a2a76cc8",
"input": "Problem: a bag contains 6 white marbles and 6 black marbles . if each of 6 girls and 6 boys randomly selects and keeps a marble , what is the probability that all of the girls select the same colored marble ? \nOptions: a ) 1 / 35 , b ) 1 / 10 , c ) 1 / 3 , d ) 1 / 462 , e ) 1 / 252",
"output": [
"d"
]
},
{
"id": "task1424-133e21ed9b3c4f92a39f227f2d116809",
"input": "Problem: the set s consists of 5 numbers : { 1 , 2,3 , 4,5 } . if all possible subsets including the null set are created and one subset is chosen at random , what is the probability that the subset has 3 or 4 as its largest number ? \nOptions: a ) 3 / 4 , b ) 3 / 8 , c ) 3 / 16 , d ) 5 / 16 , e ) 3 / 32",
"output": [
"b"
]
},
{
"id": "task1424-b553027ade4744e99133c6eccd0a392c",
"input": "Problem: a basket contains 9 apples , of which 1 is spoiled and the rest are good . if we select 2 apples from the basket simultaneously and at random , what is the probability that the 2 apples selected will include the spoiled apple ? \nOptions: a ) 2 / 3 , b ) 2 / 5 , c ) 2 / 7 , d ) 2 / 9 , e ) 2 / 11",
"output": [
"d"
]
},
{
"id": "task1424-de64b3f54adb487581767ebf0fb12418",
"input": "Problem: in how many ways can 11 books on english and 9 books on french be placed in a row on a shelf so that two books on french may not be together ? \nOptions: a ) 220 . , b ) 240 , c ) 260 , d ) 280 , e ) 300",
"output": [
"a"
]
},
{
"id": "task1424-464fe74797294baa90131dd001b96738",
"input": "Problem: the odds in favour of an events are 3 : 5 . the probability of occurrence of the event is \nOptions: a ) 3 / 8 , b ) 2 / 7 , c ) 1 / 3 , d ) 2 / 5 , e ) 6 / 7",
"output": [
"a"
]
},
{
"id": "task1424-080bade8ab894787b109b3daad147dad",
"input": "Problem: in a single throw of a die , what is the probability of getting a number greater than 4 ? \nOptions: a ) 1 / 3 , b ) 1 / 4 , c ) 2 / 3 , d ) 2 / 5 , e ) 3 / 7",
"output": [
"a"
]
},
{
"id": "task1424-da3b75c7aad043a29016598dce3fa0eb",
"input": "Problem: a card is drawn from a pack of 52 cards . the probability of getting a queen club or a king of heart ? \nOptions: a ) 3 / 26 , b ) 1 / 26 , c ) 4 / 26 , d ) 6 / 26 , e ) 10 / 26",
"output": [
"b"
]
},
{
"id": "task1424-e0ff2237c59c4338a182ccda4eb54f5a",
"input": "Problem: a card is drawn from a pack of 52 cards . the probability of getting a face card ? \nOptions: a ) 2 / 15 , b ) 2 / 13 , c ) 1 / 15 , d ) 4 / 13 , e ) 5 / 7",
"output": [
"d"
]
},
{
"id": "task1424-0c70b5c2147740db99bf31290ec8cdd1",
"input": "Problem: an urn contains 5 red , 6 blue and 8 green balls . 3 balls are randomly selected from the urn , find the probability that the drawn ball are blue ? \nOptions: a ) 20 / 969 , b ) 20 / 875 , c ) 21 / 876 , d ) 3 / 512 , e ) 2 / 9",
"output": [
"a"
]
},
{
"id": "task1424-cfc89b8beb65400b802552b890665760",
"input": "Problem: the letters o , l and t are rearranged to form the word ' lot ' . find its probability . \nOptions: a ) 1 / 18 , b ) 1 / 12 , c ) 1 / 4 , d ) 1 / 8 , e ) 1 / 6",
"output": [
"e"
]
},
{
"id": "task1424-5799e5b75ea24b0090df5b1eeb5758bf",
"input": "Problem: out of 15 students in a class , 7 are from maharashtra , 5 are from karnataka , and 3 are from goa . four students are to be selected at random . what are the chances that at least one is from karnataka ? \nOptions: a ) 12 / 13 , b ) 11 / 13 , c ) 10 / 15 , d ) 1 / 15 , e ) 4 / 14",
"output": [
"b"
]
},
{
"id": "task1424-6c3e5fb9deb04ea2a3932135ade06aa4",
"input": "Problem: an urn contains 5 red , 6 blue and 8 green balls . 3 balls are randomly selected from the urn , find the probability that the drawn ball are 2 blue and 1 red ? \nOptions: a ) 25 / 323 , b ) 21 / 969 , c ) 28 / 989 , d ) 74 / 879 , e ) 23 / 589",
"output": [
"a"
]
},
{
"id": "task1424-10f93ea9288445c39fbb0be2044260fd",
"input": "Problem: a classroom has 3 electric lamps . from a collocation of 10 electric bulbs of which 6 are good , 3 are selected at random and put in the lamps . find the probability that the room is lighted . \nOptions: a ) 1 / 6 , b ) 4 / 120 , c ) 29 / 30 , d ) 1 / 9 , e ) none of these",
"output": [
"c"
]
},
{
"id": "task1424-ee9100e69b934a8493c9735cbe13143a",
"input": "Problem: there are 8 students . 4 of them are men and 4 of them are women . if 4 students are selected from the 8 students . what is the probability that the number of men is equal to that of women ? \nOptions: a ) 18 / 35 , b ) 16 / 35 , c ) 14 / 35 , d ) 13 / 35 , e ) 12 / 35",
"output": [
"a"
]
},
{
"id": "task1424-4b661da1b1a04e0babc67a8b8e857b1e",
"input": "Problem: a , b , c , d , e , f , g , h sitting in a row what is the probability that a , b , c sitting together ? \nOptions: a ) 3 / 14 , b ) 5 / 28 , c ) 3 / 28 , d ) 1 / 7 , e ) 9 / 28",
"output": [
"c"
]
},
{
"id": "task1424-a4f8909cd1c44888b2ae69a547ca7e73",
"input": "Problem: a , b , c , d , e , f , g , h sitting in a row what is the probability that a , b , d are sitting together ? \nOptions: a ) 1 / 5 , b ) 3 / 28 , c ) 1 / 7 , d ) 1 / 14 , e ) 5 / 28",
"output": [
"b"
]
},
{
"id": "task1424-fb92ca4c3d30421bac8ad72eae001dc5",
"input": "Problem: in a garden , there are yellow and green flowers which are straight and curved . if the probability of picking a green flower is 3 / 4 and picking a straight flower is 1 / 2 , then what is the probability of picking a flower which is yellow and curved \nOptions: a ) 1 / 8 , b ) 1 / 6 , c ) 1 / 4 , d ) 3 / 4 , e ) 7 / 8",
"output": [
"a"
]
},
{
"id": "task1424-49662f44299c4d6aa0dc2a8121427ec6",
"input": "Problem: in a throw of dice what is the probability of ge æ « ng number greater than 4 \nOptions: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 5 , d ) 1 / 6 , e ) none of these",
"output": [
"b"
]
},
{
"id": "task1424-8f48d2c29ff14039afff1a408e31fdc0",
"input": "Problem: in a certain animal population , for each of the first 3 months of life , the probability that an animal will die during that month is 1 / 10 . for a group of 150 newborn members of the population , approximately how many would be expected to survive the first 3 months of life ? \nOptions: a ) 110 , b ) 146 , c ) 152 , d ) 162 , e ) 170",
"output": [
"a"
]
},
{
"id": "task1424-a629255292ae45979e1fba97068d5d43",
"input": "Problem: a bag contains 4 white marbles and 4 black marbles . if each of 4 girls and 4 boys randomly selects and keeps a marble , what is the probability that all of the girls select the same colored marble ? \nOptions: a ) 1 / 35 , b ) 1 / 9 , c ) 1 / 10 , d ) 1 / 20 , e ) 1 / 30",
"output": [
"a"
]
},
{
"id": "task1424-10870460566b45d0885fea71111a60c4",
"input": "Problem: there is a 5 % chance that tigers will not win at all during the whole season . there is a 5 % chance that federer will not play at all in the whole season . what is the greatest possible probability that the tigers will win and federer will play during the season ? \nOptions: a ) 55 % , b ) 60 % , c ) 70 % , d ) 72 % , e ) 95 %",
"output": [
"e"
]
},
{
"id": "task1424-ab8bd13f98284bee9141212b0c73e0fb",
"input": "Problem: a letter lock consists of 3 rings each marked with 6 different letters . the number of distinct unsuccessful attempts to open the lock is at the most - . \nOptions: a ) 216 , b ) 243 , c ) 215 , d ) 729 , e ) 728",
"output": [
"c"
]
},
{
"id": "task1424-8102fa1c95754eae88856d39957549d6",
"input": "Problem: a number is selected at random from the first 30 natural numbers . what is the probability that the number is a multiple of either 3 or 17 ? \nOptions: a ) 17 / 30 , b ) 2 / 5 , c ) 7 / 15 , d ) 4 / 15 , e ) 11 / 30",
"output": [
"e"
]
},
{
"id": "task1424-1608cf2809254e669261a486c2b8436b",
"input": "Problem: find the probability that a leap year chosen at random will have 53 sundays \nOptions: a ) 2 / 7 , b ) 2 / 6 , c ) 2 / 5 , d ) 2 / 3 , e ) 2 / 4",
"output": [
"a"
]
},
{
"id": "task1424-46ddd799aefd4e09a03838adb8b5fa57",
"input": "Problem: a bag contains 3 blue and 5 white marbles . one by one , marbles are drawn out randomly until only two are left in the bag . what is the probability q that out of the two , one is white and one is blue ? \nOptions: a ) 15 / 56 , b ) 41 / 56 , c ) 13 / 28 , d ) 15 / 28 , e ) 5 / 14",
"output": [
"d"
]
},
{
"id": "task1424-e7c64dbb053f43e2a0f860709d7b7a1f",
"input": "Problem: from a pack of 52 cards , 1 card is drawn at random . find the probability of a face card drawn \nOptions: a ) 4 / 13 , b ) 1 / 52 , c ) 1 / 4 , d ) 1 / 5 , e ) none of above",
"output": [
"a"
]
},
{
"id": "task1424-bae5833492e14c03895d5483d5a04715",
"input": "Problem: a man speaks truth 3 out of 4 times . he throws a die and reports it to be a 6 . what is the probability of it being a 6 ? \nOptions: a ) 3 / 5 , b ) 1 / 2 , c ) 3 / 4 , d ) 3 / 8 , e ) 3 / 6",
"output": [
"d"
]
},
{
"id": "task1424-c75c6a08a5994ec48c417fe185cb4df7",
"input": "Problem: in how many ways can 22 books on english and 20 books on hindi be placed in a row on a shelf so that two books on hindi may not be together ? \nOptions: a ) 4586 , b ) 5896 , c ) 2415 , d ) 1771 , e ) 1881",
"output": [
"d"
]
},
{
"id": "task1424-9c7ed1797177485b88a1b0565081c718",
"input": "Problem: a box contains 4 red balls and 4 black balls . one by one , every ball is selected at random without replacement . what is the probability that the fourth ball selected is black ? \nOptions: a ) 1 / 4 , b ) 1 / 2 , c ) 1 / 2 , d ) 5 / 8 , e ) 2",
"output": [
"e"
]
},
{
"id": "task1424-b5c269d9f0a24eaf9e2d7161ae585f0d",
"input": "Problem: in a department store prize box , 40 % of the notes give the winner a dreamy vacation ; the other notes are blank . what is the approximate probability that 3 out of 5 people that draw the notes one after the other , and immediately return their note into the box get a dreamy vacation ? \nOptions: a ) 0.12 , b ) 0.23 , c ) 0.35 , d ) 0.45 , e ) 0.65",
"output": [
"b"
]
},
{
"id": "task1424-7d5caba597ec4ee6a39cc52753f32e31",
"input": "Problem: in how many ways can 5 people be arranged in a circle ? \nOptions: a ) 2 ! , b ) 5 ! , c ) 4 ! , d ) 3 ! , e ) 6 !",
"output": [
"c"
]
},
{
"id": "task1424-6f1824f824754474861612f7e2258e4b",
"input": "Problem: a jar contains only red , yellow , and orange marbles . if there are 3 red , 5 yellow , and 4 orange marbles , and 3 marbles are chosen from the jar at random without replacing any of them , what is the probability that 2 yellow , 1 red , and no orange marbles will be chosen ? \nOptions: a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 5 / 22",
"output": [
"d"
]
},
{
"id": "task1424-b862ff3f26d84c4a870cba90e8fbcdde",
"input": "Problem: in a full deck of 52 cards , there are 13 spades . a game is played whereby a card from is chosen at random from the deck . if the card is a spade , a winner is declared . if the card is not a spade , it is returned to the deck , the deck is reshuffled and another card is drawn . this process is repeated until a spade is drawn . what is the probability that one will pick the first spade on the second draw or later ? \nOptions: a ) 1 / 8 , b ) 1 / 4 , c ) 1 / 2 , d ) 3 / 4 , e ) 7 / 8",
"output": [
"d"
]
},
{
"id": "task1424-d81e0a1791ca4a3190702d800b7efda5",
"input": "Problem: six 6 faced dice are thrown together . the probability that all the three show the same number on them is ? \nOptions: a ) 1 / 32 , b ) 1 / 7776 , c ) 1 / 33 , d ) 1 / 38 , e ) 1 / 34",
"output": [
"b"
]
},
{
"id": "task1424-b7bed29ffc1c49e9819aeb9d3fbf0552",
"input": "Problem: a player holds 13 cards of 4 suits , of which 7 are black and 6 are red . there are twice as many diamonds as spades and twice as many hearts as diamonds . how many clubs does he hold \nOptions: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8",
"output": [
"c"
]
},
{
"id": "task1424-d15212f8f1924ff69163b05fc5ebf383",
"input": "Problem: there are 7 girls and 3 chairs . in how many ways girls can occupy the chairs ? \nOptions: a ) 760 , b ) 210 , c ) 560 , d ) 740 , e ) 800",
"output": [
"b"
]
},
{
"id": "task1424-dca95bdc0b4d45de8bba3f021f448b51",
"input": "Problem: two cards are drawn together from a pack of 52 cards . the probability that one is a spade and one is a heart , is : \nOptions: a ) 2 / 109 , b ) 7 / 109 , c ) 8 / 223 , d ) 14 / 263 , e ) 13 / 102",
"output": [
"e"
]
},
{
"id": "task1424-28625533faac44409d9b45771e149fb5",
"input": "Problem: what is the probability of getting only 1 head in a single throw of four fair coins ? \nOptions: a ) 1 / 2 , b ) 3 / 8 , c ) 1 / 4 , d ) 1 / 5 , e ) 5 / 8",
"output": [
"c"
]
},
{
"id": "task1424-e680cd1fb6fa4128a4069ed08a46d087",
"input": "Problem: what is the smallest number by which 2880 must be divided in order to make it into a perfect square ? \nOptions: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7",
"output": [
"c"
]
},
{
"id": "task1424-e21f42023c3949109ca5d046904b0154",
"input": "Problem: a quiz has one mcq question with a , b and c as options . and two questions with true / false answers . what is the probability of giving all 3 answers correct ? \nOptions: a ) 1 / 12 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 2 , e ) 1 / 6",
"output": [
"a"
]
},
{
"id": "task1424-4f80eb58257d4483a0f59619e3650641",
"input": "Problem: what is the probability of getting exactly 2 heads in a single throw of five fair coins ? \nOptions: a ) 1 / 4 , b ) 3 / 8 , c ) 3 / 16 , d ) 5 / 16 , e ) 11 / 32",
"output": [
"d"
]
},
{
"id": "task1424-e16007ea71a1466f8613136a1aa070b2",
"input": "Problem: a child want to buy 3 new toys . if there are 10 toys that satisfy the child ' s criteria , in how many different ways can the child select the 3 new toys if the order of selection does n ' t matter . \nOptions: a ) 20 , b ) 120 , c ) 210 , d ) 15 , e ) 45",
"output": [
"b"
]
},
{
"id": "task1424-e7deabf5f0c044e8ae3cdfa7ecb444ba",
"input": "Problem: a coin is tossed 7 times . what is the probability of getting exactly 6 heads ? \nOptions: a ) 7 / 32 , b ) 3 / 64 , c ) 5 / 64 , d ) 3 / 128 , e ) 7 / 128",
"output": [
"e"
]
},
{
"id": "task1424-63cd78ebd8b24508a335802f5cc75c74",
"input": "Problem: set a contains 4 different positive odd integers and 6 different positive even integers . set b contains two different positive odd integers and 3 different positive even integers . if one integer from set a and one integer from set b are chosen at random , what is the probability that the product of the chosen integers is even ? \nOptions: a ) 3 / 5 , b ) 4 / 5 , c ) 17 / 25 , d ) 21 / 25 , e ) 43 / 50",
"output": [
"d"
]
},
{
"id": "task1424-146748176ecf418aaf3f1cdf909ff00d",
"input": "Problem: a certain junior class has 1,000 students and a certain senior class has 800 students . among these students , there are 40 siblings pairs , each consisting of 1 junior and 1 senior . if 1 student is to be selected at random from each class , what is the probability that the 2 students selected at will be a sibling pair ? \nOptions: a ) 3 / 40,000 , b ) 1 / 3,600 , c ) 1 / 20,000 , d ) 1 / 60 , e ) 1 / 15",
"output": [
"c"
]
},
{
"id": "task1424-124c2795cc6c4f6487624d89a232c406",
"input": "Problem: 8 coins are tossed . whats is the probability that one and only one turns up head ? \nOptions: a ) 1 / 256 , b ) 1 / 32 , c ) 1 / 64 , d ) 1 / 128 , e ) 1 / 189",
"output": [
"b"
]
},
{
"id": "task1424-9921a0f85d3b4989afb4cbed78a8030e",
"input": "Problem: how many positive integers less than 600 can be formed using the numbers 1 , 2 , 3 and 5 for the digits ? \nOptions: a ) 48 , b ) 52 , c ) 66 , d ) 68 , e ) 84",
"output": [
"e"
]
},
{
"id": "task1424-668cbe3991694312a7b9928ea7cf0f77",
"input": "Problem: in a bag containing 3 balls , a white ball was placed and then 1 ball was taken out at random . what is the probability that the extracted ball would turnon to be white , if all possible hypothesis concerning thecolor of theballs that initiallyin the bag were equally possible ? \nOptions: a ) 2 / 3 , b ) 5 / 8 , c ) 3 / 5 , d ) 3 / 8 , e ) 4 / 9",
"output": [
"b"
]
},
{
"id": "task1424-1bc1219223584841bb65b2435b560666",
"input": "Problem: a box contains 100 balls , numbered from 1 to 100 . if 3 balls are selected at random and with replacement from the box . if the 3 numbers on the balls selected contain two odd and one even . what is the probability r that the first ball picked up is odd numbered ? \nOptions: a ) 0 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 1",
"output": [
"d"
]
},
{
"id": "task1424-85d341cf56c64cfbbe2d84a6d7b5b45e",
"input": "Problem: a number is selected at random from the first 30 natural numbers . what is the probability that the number is a multiple of either 4 or 15 ? \nOptions: a ) 17 / 30 , b ) 2 / 5 , c ) 3 / 10 , d ) 4 / 15 , e ) 11 / 30",
"output": [
"c"
]
},
{
"id": "task1424-4d5fbb680acd417a9ee473c96fac4823",
"input": "Problem: there are 15 boys and 10 girls in a class . if three students are selected at random , in how many ways that 1 girl or 2 boys are selected ? \nOptions: a ) 100 , b ) 105 , c ) 115 , d ) 120 , e ) 125",
"output": [
"c"
]
},
{
"id": "task1424-b62873013414426293ea2d785ad9cc9b",
"input": "Problem: 6 animals of a circus has to be placed inside in 6 cages one in each cage . if 4 of the cage are too small for 6 of the animal then find the number of ways of caging the animal . \nOptions: a ) a . 240 , b ) b . 808250 , c ) c . 502450 , d ) d . 784200 , e ) e . 302400",
"output": [
"a"
]
},
{
"id": "task1424-51b207480e7b4b8598f4ab10e022363f",
"input": "Problem: in a throw of dice what is the probability of ge æ « ng number greater than 3 \nOptions: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 5 , d ) 1 / 6 , e ) none of these",
"output": [
"a"
]
},
{
"id": "task1424-650b189c6d7a44deaf6579d137d79bed",
"input": "Problem: a card is drawn from a pack of 52 cards . the probability of getting a queen of spade or an ace of club is : \nOptions: a ) 1 / 13 , b ) 1 / 26 , c ) 2 / 13 , d ) 1 / 52 , e ) 1 / 48",
"output": [
"b"
]
},
{
"id": "task1424-0132ba3929d74793929fa3e1cd8b52c4",
"input": "Problem: a bag consists of 20 marbles , of which 5 are blue , 7 are red , and the remainder are white . if lisa is to select a marble from the bag at random , what is the probability that the marble will be red or white ? \nOptions: a ) 3 / 4 , b ) 2 / 4 , c ) 1 / 4 , d ) 1 / 8 , e ) 1 / 16",
"output": [
"a"
]
},
{
"id": "task1424-f97610879bf845f3a14e779a0d8713e6",
"input": "Problem: in how many ways 4 boys and 3 girls can be seated in a row so that they are alternative ? \nOptions: a ) 120 , b ) 144 , c ) 160 , d ) 210 , e ) 180",
"output": [
"b"
]
},
{
"id": "task1424-61fdd364d6bd4606afe3f8841b3d13ff",
"input": "Problem: on a ranch , a rancher can place a loop of rope , called a lasso , once in every 2 throws around a cow ’ s neck . what is the probability that the rancher will be able to place a lasso around a cow ’ s neck at least once in 3 attempts ? \nOptions: a ) 3 / 4 , b ) 5 / 8 , c ) 7 / 8 , d ) 9 / 16 , e ) 15 / 16",
"output": [
"c"
]
},
{
"id": "task1424-8564a654d65e41c1b01a65891cf9e937",
"input": "Problem: in a lottery there are 10 prizes and 25 blanks . a lottery is drawn at random . what is the probability of getting a blank ? \nOptions: a ) 2 / 3 , b ) 6 / 7 , c ) 5 / 7 , d ) 8 / 7 , e ) 4 / 3",
"output": [
"c"
]
},
{
"id": "task1424-e3b0f2393b1f4bcfa9dfb9e9fb4c38a4",
"input": "Problem: kim has 4 pairs of shoes ; each pair is a different color . if kim randomly selects 2 shoes without replacement from the 8 shoes , what is the probability that she will select 2 shoes of the same color ? \nOptions: a ) 1 / 7 , b ) 1 / 8 , c ) 1 / 9 , d ) 1 / 10 , e ) 1 / 25",
"output": [
"a"
]
},
{
"id": "task1424-884c07041ba14bd7a0c8afa22813dad9",
"input": "Problem: a fair coin is tossed 4 times . what is the probability of getting at least 2 tails ? \nOptions: a ) 1 / 16 , b ) 1 / 2 , c ) 3 / 16 , d ) 11 / 16 , e ) 3 / 8",
"output": [
"d"
]
},
{
"id": "task1424-a69b7ed857144145aac7c479f2a8d959",
"input": "Problem: out of 10 students in a class , 4 are from maharashtra , 3 are from karnataka , and 3 are from goa . four students are to be selected at random . what are the chances that at least one is from karnataka ? \nOptions: a ) 1 / 3 , b ) 4 / 9 , c ) 5 / 6 , d ) 3 / 7 , e ) 1 / 4",
"output": [
"c"
]
},
{
"id": "task1424-411d741be0e240f2a753dab1f8f0dcef",
"input": "Problem: persons a and b . person a picks a random no . from 1 to 1000 . then person b picks a random no . from 1 to 1000 . what is the probability of b getting no . greater then what a has picked . \nOptions: a ) 0.3995 , b ) 0.4995 , c ) 0.5995 , d ) 0.6995 , e ) 0.7995",
"output": [
"b"
]
},
{
"id": "task1424-43f64242dcf146199adab984b69b9aed",
"input": "Problem: find the probability that a number selected from numbers 1 , 2 , 3 , . . . , 30 is a prime number , when each of the given numbers is equally likely to be selected ? \nOptions: a ) 10 / 30 , b ) 1 / 30 , c ) 8 / 30 , d ) 3 / 30 , e ) 7 / 30",
"output": [
"c"
]
},
{
"id": "task1424-679a7df48344403cb39d9eaea09656be",
"input": "Problem: there is a 20 % chance sandy will visit china this year , while there is a 60 % chance that she will visit malaysia this year . what is the probability that sandy will visit either china or malaysia this year , but not both ? \nOptions: a ) 40 % , b ) 48 % , c ) 56 % , d ) 64 % , e ) 72 %",
"output": [
"c"
]
},
{
"id": "task1424-8a326ef266e34dbc9877bb2a09b5e957",
"input": "Problem: a certain junior class has 1,000 students and a certain senior class has 800 students . among these students , there are 20 siblings pairs , each consisting of 1 junior and 1 senior . if 1 student is to be selected at random from each class , what is the probability that the 2 students selected at will be a sibling pair ? \nOptions: a ) 3 / 40,000 , b ) 1 / 3,600 , c ) 9 / 2,000 , d ) 1 / 40,000 , e ) 1 / 15",
"output": [
"d"
]
},
{
"id": "task1424-efded02456e243e6bb58ea89575a1781",
"input": "Problem: the membership of a committee consists of 4 english teachers , 2 mathematics teachers , and 2 social studies teachers . if 2 committee members are to be selected at random to write the committee ’ s report , what is the probability that the two members selected will both be english teachers ? \nOptions: a ) 2 / 3 , b ) 1 / 3 , c ) 2 / 9 , d ) 1 / 12 , e ) 3 / 28",
"output": [
"e"
]
},
{
"id": "task1424-b68d11d5008a49f3944488fbb98f8105",
"input": "Problem: x , y , and z are all unique numbers . if x is chosen randomly from the set { 8 , 9 , 10 , 11 } and y and z are chosen randomly from the set { 20 , 21 , 22 , 23 } , what is the probability that x and y are prime and z is not ? \nOptions: a ) 1 / 16 , b ) 3 / 11 , c ) 13 / 20 , d ) 3 / 10 , e ) 1 / 10",
"output": [
"a"
]
},
{
"id": "task1424-e1677e74867e4baaaa8bfc3c6175ce41",
"input": "Problem: a child want to buy 5 new toys . if there are 15 toys that satisfy the child ' s criteria , in how many different ways can the child select the 5 new toys if the order of selection does n ' t matter . \nOptions: a ) 210 , b ) 1365 , c ) 3003 , d ) 5005 , e ) 3030",
"output": [
"c"
]
},
{
"id": "task1424-8a4c3f5431e24151b229872f1439b4a0",
"input": "Problem: three coins are tossed . find the probability of at least 2 tails ? \nOptions: a ) 1 / 2 , b ) 2 / 3 , c ) 1 / 4 , d ) 1 / 8 , e ) 3 / 8",
"output": [
"a"
]
},
{
"id": "task1424-c93698d563f749c186a1b929ee87a0e2",
"input": "Problem: jane and thomas are among the 6 people from which a committee of 3 people is to be selected . how many different possible committees of 3 people can be selected from these 6 people if at least one of either jane or thomas is to be selected ? \nOptions: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20",
"output": [
"c"
]
},
{
"id": "task1424-e3ea81909a1244eab7a1742e5ddef89c",
"input": "Problem: a meeting has to be conducted with 5 managers . find the number of ways in which the managers may be selected from among 7 managers , if there are 2 managers who refuse to attend the meeting together . \nOptions: a ) 6 , b ) 8 , c ) 10 , d ) 11 , e ) 15",
"output": [
"d"
]
},
{
"id": "task1424-2e24383cb2c44a4cb40eb9edf9c4181f",
"input": "Problem: in how many ways 4 boys and 5 girls can be seated in a row so that they are alternate . \nOptions: a ) 144 , b ) 288 , c ) 12 , d ) 256 , e ) 2880",
"output": [
"e"
]
},
{
"id": "task1424-c08527f2636943548f74a5012bde08ca",
"input": "Problem: two mba admissions committees are to be formed randomly from 6 second year mbas with 3 members each . what is the probability e that jane will be on the same committee as albert ? \nOptions: a ) 12 % , b ) 20 % , c ) 33 % , d ) 40 % , e ) 50 %",
"output": [
"d"
]
},
{
"id": "task1424-df873079008743069f7b08ffc0ba00ce",
"input": "Problem: the chance of rain on any given day in tel - aviv is 50 % . what is the probability q that it rained in tel - aviv on exactly 4 out of 6 randomly chosen days ? \nOptions: a ) 15 / 64 , b ) 30 / 64 , c ) 1 / 2 , d ) 1 / 4 , e ) 52 / 64",
"output": [
"a"
]
},
{
"id": "task1424-b12285e0325d4d5ea96ccfff083b3a7f",
"input": "Problem: a fair coin is tossed 5 times . what is the probability of getting more heads than tails in 5 tosses ? \nOptions: a ) 1 / 2 , b ) 63 / 128 , c ) 4 / 7 , d ) 61 / 256 , e ) 63 / 64",
"output": [
"a"
]
},
{
"id": "task1424-7e1b900b2fe74d84b40bc3fb8d7bfe8f",
"input": "Problem: a bag contains 3 red , 5 yellow and 4 green balls . 3 balls are drawn randomly . what is the probability that balls drawn contain exactly two green balls ? \nOptions: a ) 9 / 16 , b ) 7 / 18 , c ) 12 / 55 , d ) 14 / 67 , e ) 19 / 87",
"output": [
"c"
]
},
{
"id": "task1424-1be008cc28644c8792b83090ebaffb6c",
"input": "Problem: kim has 3 pairs of shoes ; each pair is a different color . if kim randomly selects 2 shoes without replacement from the 6 shoes , what is the probability that she will select 2 shoes of the same color ? \nOptions: a ) 2 / 5 , b ) 1 / 5 , c ) 1 / 9 , d ) 1 / 10 , e ) 1 / 25",
"output": [
"b"
]
},
{
"id": "task1424-95781bb9c86a4e3c8c7475a26a2dd80c",
"input": "Problem: there are 13 boys and 10 girls in a class . if three students are selected at random , in how many ways that 1 girl & 2 boys are selected ? \nOptions: a ) 120 , b ) 480 , c ) 780 , d ) 720 , e ) 800",
"output": [
"c"
]
},
{
"id": "task1424-8e931a7c941b4b0a9cb26c5859769b8c",
"input": "Problem: joe has candys on his pocket , 4 of those candies have lemon flavor , and 3 have caramel flavor . if joe take one , what is the probability that he picks one caramel flavor ? \nOptions: a ) 1 , b ) 2 , c ) none , d ) 3 / 7 , e ) 3 / 4",
"output": [
"d"
]
},
{
"id": "task1424-a82a7616d2974061b72a1cd40209e438",
"input": "Problem: there is a 50 % chance jen will visit chile this year , while there is a 50 % chance that she will visit madagascar this year . what is the probability that jen will visit either chile or madagascar this year , but not both ? \nOptions: a ) 25.0 % , b ) 50.0 % , c ) 62.5 % , d ) 75.0 % , e ) 80.0 %",
"output": [
"b"
]
},
{
"id": "task1424-ee3055c731914ffcb6845e8eae815d95",
"input": "Problem: what is the probability that the sum of two dice will yield a 5 , and then when both are thrown again , their sum will again yield a 5 ? assume that each die has 4 sides with faces numbered 1 to 4 . \nOptions: a ) 1 / 144 , b ) 1 / 36 , c ) 1 / 12 , d ) 1 / 16 , e ) 1 / 3",
"output": [
"d"
]
},
{
"id": "task1424-6670389f972149beb930edcded181de7",
"input": "Problem: wink , inc . follows a certain procedure that requires two tasks to be finished independently in order for a job to be done . on any given day , there is a 5 / 8 probability that task 1 will be completed on time , and a 3 / 5 probability that task 2 will be completed on time . on a certain day , what is the probability that task 1 will be completed on time , but task 2 will not ? \nOptions: a ) 1 / 4 , b ) 3 / 40 , c ) 13 / 40 , d ) 7 / 20 , e ) 13 / 22",
"output": [
"a"
]
},
{
"id": "task1424-bd4bacc799994aabb439c8e9ed908a83",
"input": "Problem: two unbiased coins are tossed . what is the probability of getting at most one head ? \nOptions: a ) 2 / 3 , b ) 1 , c ) 3 / 4 , d ) 2 , e ) 1 / 2",
"output": [
"c"
]
},
{
"id": "task1424-b7e20640338a4f8faacc9aa80177d75f",
"input": "Problem: there are 8 books on a shelf , of which 3 are paperbacks and 5 are hardbacks . how many possible selections of 4 books from this shelf include at least one paperback ? \nOptions: a ) a ) 40 , b ) b ) 45 , c ) c ) 50 , d ) d ) 55 , e ) e ) 65",
"output": [
"e"
]
},
{
"id": "task1424-be139f3a13e44491a787dc6176f3cd7c",
"input": "Problem: a store has 10 bottles of juice , including 6 bottles of apple juice . in the evening , 6 bottles of juice are sold one by one . what is the probability of selling 4 bottles of apple juice among the 6 bottles ? assume that every bottle has an equal chance of being bought . \nOptions: a ) 2 / 5 , b ) 3 / 5 , c ) 2 / 3 , d ) 1 / 2 , e ) 3 / 7",
"output": [
"e"
]
},
{
"id": "task1424-802184644de949ac853c719aff44a680",
"input": "Problem: five 6 faced dice are thrown together . the probability that all the three show the same number on them is ? \nOptions: a ) 1 / 32 , b ) 1 / 1296 , c ) 1 / 33 , d ) 1 / 38 , e ) 1 / 34",
"output": [
"b"
]
},
{
"id": "task1424-e5b75e3f812941cf96b9abbbf5748af8",
"input": "Problem: what is the probability that a two digit number selected at random will be a multiple of ' 3 ' and not a multiple of ' 5 ' ? \nOptions: a ) 2 / 15 , b ) 4 / 15 , c ) 1 / 15 , d ) 4 / 90 , e ) 5 / 60",
"output": [
"b"
]
},
{
"id": "task1424-28ba98ddfa454874ba791dd05e441154",
"input": "Problem: what is the probability of getting a sum of 12 when rolling 3 dice simultaneously ? \nOptions: a ) 10 / 216 , b ) 12 / 216 , c ) 21 / 216 , d ) 23 / 216 , e ) 25 / 216",
"output": [
"e"
]
},
{
"id": "task1424-a9a612e6158542c1859e8d8e459f7ab4",
"input": "Problem: lola rolls a die 3 times . what is the probability that she gets a 4 on the last one of the 3 rolls ? \nOptions: a ) 215 / 216 , b ) 216 , c ) 1 / 216 , d ) none , e ) 2",
"output": [
"a"
]
},
{
"id": "task1424-4adef95ad965464b859b203dabc712dd",
"input": "Problem: find the probability that a year chosen at random has 53 mondays . \nOptions: a ) 5 / 28 , b ) 3 / 28 , c ) 1 / 28 , d ) 3 / 28 , e ) 3 / 27",
"output": [
"a"
]
},
{
"id": "task1424-c7ceddb3d8e04c8b82d04f8640cdb64d",
"input": "Problem: if 4 people are selected from a group of 6 married couples , what is the probability that none of them would be married to each other ? \nOptions: a ) 1 / 33 , b ) 2 / 33 , c ) 1 / 3 , d ) 16 / 33 , e ) 11 / 12",
"output": [
"d"
]
},
{
"id": "task1424-ab2b3230846b440c8ef1ae89ba6c461d",
"input": "Problem: if a coin is flipped , the probability that the coin will land heads is 1 / 2 . if the coin is flipped 6 times , what is the probability that it will land heads up on all 6 flips ? \nOptions: a ) 1 / 6 , b ) 1 / 8 , c ) 1 / 32 , d ) 1 / 2 , e ) 1 / 64",
"output": [
"e"
]
},
{
"id": "task1424-0c8389dffe394ba4831bee120074dad1",
"input": "Problem: what is the probability of getting exactly 4 heads in a single throw of five fair coins ? \nOptions: a ) 1 / 4 , b ) 3 / 8 , c ) 3 / 16 , d ) 5 / 32 , e ) 7 / 32",
"output": [
"d"
]
},
{
"id": "task1424-b6df8e1d22664606995c406e88d2b107",
"input": "Problem: if two integers x , y ( x > y ) are selected from - 10 to 11 ( inclusive ) , how many possible cases are there ? \nOptions: a ) 150 , b ) 180 , c ) 190 , d ) 210 , e ) 231",
"output": [
"e"
]
},
{
"id": "task1424-2596011f563847dca7a57c2f659637d7",
"input": "Problem: find the probability that a leap year selected at random will have 53 sundays \nOptions: a ) 6 / 7 , b ) 5 / 7 , c ) 4 / 7 , d ) 3 / 7 , e ) 2 / 7",
"output": [
"e"
]
},
{
"id": "task1424-7f0af0fdc95848c4a38954d329432d2b",
"input": "Problem: there are 10 pairs of socks and 2 socks are worn from that such that the pair of socks worn are not of the same pair . what is the number of pair that can be formed . \nOptions: a ) 90 , b ) 85 , c ) 75 , d ) 95 , e ) 82",
"output": [
"a"
]
},
{
"id": "task1424-73ca0d8523f342d5a16c79a27365dc27",
"input": "Problem: a number is selected at random from the first 30 natural numbers . what is the probability that the number is a multiple of either 5 or 12 ? \nOptions: a ) 17 / 30 , b ) 2 / 5 , c ) 7 / 15 , d ) 4 / 15 , e ) 11 / 30",
"output": [
"d"
]
},
{
"id": "task1424-adf7ed55afb94f0aa9d9e10c089b2a68",
"input": "Problem: in a certain animal population , for each of the first 3 months of life , the probability that an animal will die during that month is 1 / 10 . for a group of 200 newborn members of the population , approximately how many would be expected to survive the first 3 months of life ? \nOptions: a ) 140 , b ) 146 , c ) 152 , d ) 162 , e ) 170",
"output": [
"b"
]
},
{
"id": "task1424-857df3992c684ae39b694b60afa8ae35",
"input": "Problem: a life insurance company insured 25,000 young boys , 14,000 young girls and 16,000 young adults . the probability of death within 10 years of a young boy , young girl and a young adult are 0.02 , 0.03 and 0.15 respectively . one insured person dies . what is the probability that the dead person is a young boy ? \nOptions: a ) 36 / 165 , b ) 25 / 166 , c ) 26 / 165 , d ) 32 / 165 , e ) 33 / 165",
"output": [
"b"
]
},
{
"id": "task1424-9d9c6958b26d402da94371e0da253085",
"input": "Problem: a box contains 100 balls , numbered from 1 to 100 . if 3 balls are selected at random and with replacement from the box . if the 3 numbers on the balls selected contain two odd and one even . what is the probability z that the first ball picked up is odd numbered ? \nOptions: a ) 0 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 1",
"output": [
"d"
]
},
{
"id": "task1424-4e0eec98b5d04fb292d25ec8330850e5",
"input": "Problem: from a pack of 52 cards , 1 card is drawn at random . what is the probability that a jack , queen , or king is drawn ? \nOptions: a ) 1 / 4 , b ) 1 / 12 , c ) 2 / 13 , d ) 3 / 13 , e ) 3 / 26",
"output": [
"d"
]
},
{
"id": "task1424-b445045228ee48ac8e4b2df96fbe2ee3",
"input": "Problem: a jar contains 5 black and 2 white balls . if you pick two balls at the same time , what ' s the probability that one ball is black and one is white ? \nOptions: a ) 2 / 7 , b ) 5 / 21 , c ) 4 / 21 , d ) 3 / 7 , e ) 1 / 2",
"output": [
"b"
]
},
{
"id": "task1424-2d94c1982f0b4f53b2e0788c4a84c69c",
"input": "Problem: a bag consists of 20 marbles , of which 5 are blue , 9 are red , and the remainder are white . if lisa is to select a marble from the bag at random , what is the probability that the marble will be red or white ? \nOptions: a ) 3 / 4 , b ) 2 / 4 , c ) 1 / 4 , d ) 1 / 8 , e ) 1 / 16",
"output": [
"a"
]
},
{
"id": "task1424-85cac41c944547fdaf987a8ac49535c2",
"input": "Problem: from a pack of 52 cards , two cards are drawn together at random . what is the probability that the one is heart and other two is diamond ? \nOptions: a ) 238 / 5525 , b ) 176 / 5534 , c ) 253 / 5523 , d ) 234 / 5525 , e ) 1 / 5525",
"output": [
"d"
]
},
{
"id": "task1424-0d73384b6e024ff884ec4c74435e271b",
"input": "Problem: how many cubes of 4 cm edge can be cut out of a cube of 28 cm edge \nOptions: a ) 343 , b ) 232 , c ) 216 , d ) 484 , e ) none of these",
"output": [
"a"
]
},
{
"id": "task1424-07900a21668047ec89148435d537a14c",
"input": "Problem: from a pack of 52 cards , two cards are drawn together at random . what is the probability of one is a spade and one is a heart ? \nOptions: a ) 102 / 102 , b ) 5 / 102 , c ) 1 / 102 , d ) 8 / 102 , e ) 13 / 102",
"output": [
"e"
]
},
{
"id": "task1424-334078e0ee754baa921c29dff3458774",
"input": "Problem: there are 7 red shoes & 3 green shoes . if two of red shoes are drawn what is the probability of getting red shoes \nOptions: a ) 1 / 13 , b ) 1 / 14 , c ) 1 / 15 , d ) 7 / 15 , e ) 7 / 16",
"output": [
"d"
]
},
{
"id": "task1424-7e756c006bfe4cc5b5798dc0a271a080",
"input": "Problem: x , y , and z are all unique numbers . if x is chosen randomly from the set { 9 , 10 , 11 } and y and z are chosen randomly from the set { 20 , 21 , 22 , 23 } , what is the probability that x and y are prime and z is not ? \nOptions: a ) 1 / 20 , b ) 1 / 12 , c ) 2 / 15 , d ) 3 / 10 , e ) 1 / 7",
"output": [
"b"
]
},
{
"id": "task1424-7d9503bff21f43ecadbab76dbf8995e5",
"input": "Problem: a coin is tossed twice if the coin shows head it is tossed again but if it shows a tail then a die is tossed . if 8 possible outcomes are equally likely . find the probability that the die shows a number greater than 4 , if it is known that the first throw of the coin results in a tail \nOptions: a ) 2 / 4 , b ) 1 / 3 , c ) 2 / 3 , d ) 3 / 6 , e ) 1 / 4",
"output": [
"b"
]
},
{
"id": "task1424-e8b907c397e341b38784d359f8c84f52",
"input": "Problem: there are 10 students named alphabetically from a to j . what is the probability that a and d do not sit together if all 10 sit around a circular table ? \nOptions: a ) 2 / 9 , b ) 2 / 5 , c ) 7 / 9 , d ) 4 / 5 , e ) 8 / 9",
"output": [
"c"
]
},
{
"id": "task1424-a97a3d69932a4abc8279db4d1bb7db58",
"input": "Problem: there are 7 red balls and 5 blue balls in a jar . if 3 balls are selected from the jar , what is the probability that 3 balls selected are red balls ? \nOptions: a ) 19 / 44 , b ) 5 / 44 , c ) 3 / 41 , d ) 13 / 44 , e ) 7 / 44",
"output": [
"e"
]
},
{
"id": "task1424-4a03133b8e81478f8f2313e97015efac",
"input": "Problem: a question paper has 2 parts , a & b , each containing 10 questions . if a student has to choose 5 from part a & 10 from part b , in how many ways can he choose the questions ? \nOptions: a ) 100 , b ) 120 , c ) 125 , d ) 350 , e ) 252",
"output": [
"e"
]
},
{
"id": "task1424-329d67732bf5497ba60584b94e195b64",
"input": "Problem: what is the probability of drawing a queen from a deck of 52 cards ? \nOptions: a ) 4 / 13 , b ) 1 / 13 , c ) 4 , d ) 1 , e ) 2 / 13",
"output": [
"b"
]
},
{
"id": "task1424-233fcc99572c462b8b625fb3befd6f9a",
"input": "Problem: in a certain animal population , for each of the first 3 months of life , the probability that an animal will die during that month is 1 / 10 . for a group of 700 newborn members of the population , approximately how many would be expected to survive the first 3 months of life ? \nOptions: a ) 511 , b ) 546 , c ) 552 , d ) 562 , e ) 570",
"output": [
"a"
]
},
{
"id": "task1424-fb039c8c79434339a268e696c97c95d2",
"input": "Problem: if 4 people are selected from a group of 9 married couples , what is the probability that none of them would be married to each other ? \nOptions: a ) 1 / 33 , b ) 2 / 85 , c ) 1 / 3 , d ) 56 / 85 , e ) 11 / 85",
"output": [
"d"
]
},
{
"id": "task1424-b352c99faa4d47a7a6035352cc6175c5",
"input": "Problem: what is the probability of getting a sum 9 from two throws of a dice ? \nOptions: a ) 1 / 6 , b ) 1 / 8 , c ) 1 / 9 , d ) 1 / 12 , e ) none of these",
"output": [
"c"
]
},
{
"id": "task1424-6a978d682aca4e7b81d6d57e40457b34",
"input": "Problem: a father purchased dress for his 3 daughters . the dresses are of same color but diff size and they are kept in dark room . what is probability that all the 3 will not choose there own dress ? \nOptions: a ) 1 / 3 , b ) 2 / 3 , c ) 1 / 2 , d ) 3 / 4 , e ) 3 / 7",
"output": [
"a"
]
},
{
"id": "task1424-b29dc13d3a014aadbcebca65ebe5fd5e",
"input": "Problem: there are 13 clubs in a full deck of 52 cards . in a certain game , you pick a card from a standard deck of 52 cards . if the card is a club , you win . if the card is not a club , the person replaces the card to the deck , reshuffles , and draws again . the person keeps repeating that process until he picks a club , and the point is to measure how many draws it took before the person picked a club and , thereby , won . what is the probability that one will pick the first club on the forth draw or later ? \nOptions: a ) 1 / 2 , b ) 3 / 4 , c ) 7 / 8 , d ) 27 / 32 , e ) 27 / 64",
"output": [
"e"
]
},
{
"id": "task1424-dcc4fca0a28b40f4a0fb7de4cb4c2627",
"input": "Problem: three unbiased coins are tossed . what is the probability of getting 2 heads and 2 tail ? \nOptions: a ) 5 / 8 , b ) 1 / 4 , c ) 3 / 8 , d ) 7 / 8 , e ) 1 / 8",
"output": [
"a"
]
},
{
"id": "task1424-5ce60cb0b2cd49ceaf114d9c31e28742",
"input": "Problem: preethi has 6 flavors of ice cream in his parlor . how many options are there for dorathy to pick a one - flavor , two - flavor , 3 - flavor , 4 - flavor , 5 flavor or 6 flavor order ? \nOptions: a ) 26 , b ) 36 , c ) 64 , d ) 67 , e ) 63",
"output": [
"e"
]
},
{
"id": "task1424-af99b5f7a9b5433da6c3c3518ca48d0a",
"input": "Problem: what is the probability of getting at least one six in a single throw of three unbiased dice ? \nOptions: a ) 1 / 6 , b ) 125 / 216 , c ) 1 / 36 , d ) 81 / 216 , e ) 91 / 216",
"output": [
"e"
]
},
{
"id": "task1424-5e38387a50d8443db619b84a7f18ab40",
"input": "Problem: what is the sum of all 5 digit numbers which can be formed with the digits 0 , 1,2 , 3,4 without repetation ? \nOptions: a ) 2599980 , b ) 235500 , c ) 923580 , d ) 765432 , e ) 765434",
"output": [
"a"
]
},
{
"id": "task1424-c05d86c5f1a2427ba7942a5a7fd38131",
"input": "Problem: if a coin is flipped , the probability that the coin will land tails is 1 / 2 . if the coin is flipped 3 times , what is the probability that it will land tails up on the first flip and not on the last 2 flips ? \nOptions: a ) 1 / 8 , b ) 1 / 4 , c ) 1 / 3 , d ) 1 / 2 , e ) 3 / 4",
"output": [
"a"
]
},
{
"id": "task1424-8c56b9670d2447798513df17e78d4ed0",
"input": "Problem: 45 girls and 60 boys are present at a party . there are 17 girl - boy are in relationship among them . if a girl and a boy is selected at random , what is the probability that they will be not a couple ? \nOptions: a ) 17 / 2900 , b ) 2683 / 2700 , c ) 2496 / 2700 , d ) 2369 / 2700 , e ) 198 / 270",
"output": [
"b"
]
},
{
"id": "task1424-076b7aae8dcc49bab5d590e77bc3b883",
"input": "Problem: what is the probability of getting a sum 9 from two throw of a dice ? \nOptions: a ) 1 / 6 , b ) 1 / 8 , c ) 1 / 9 , d ) 1 / 12 , e ) 1 / 13",
"output": [
"c"
]
},
{
"id": "task1424-470965bafacf462680735ae62f137037",
"input": "Problem: if two integers x , y ( x > y ) are selected from - 10 to 5 ( inclusive ) , how many possible cases are there ? \nOptions: a ) 105 , b ) 120 , c ) 190 , d ) 210 , e ) 240",
"output": [
"b"
]
},
{
"id": "task1424-7f40c0dd32f24e419ecb2a6348e4fd7c",
"input": "Problem: there are 6 red shoes & 4 green shoes . if two of red shoes are drawn what is the probability of getting red shoes \nOptions: a ) 1 / 3 , b ) 1 / 4 , c ) 1 / 2 , d ) 1 / 5 , e ) 1 / 6",
"output": [
"a"
]
},
{
"id": "task1424-089ae940832740ae99a43538400fc8b5",
"input": "Problem: a certain junior class has 100 students and a certain senior class has 80 students . among these students , there are 6 siblings pairs each consisting of 1 junior and 1 senior . if 1 student is to be selected at random from each class , what is the probability that the 2 students selected will be a sibling pair ? \nOptions: a ) 3 / 40000 , b ) 1 / 3600 , c ) 9 / 2000 , d ) 3 / 4000 , e ) 1 / 15",
"output": [
"d"
]
},
{
"id": "task1424-bf004bd8bb0d4c36a3081393ee73ddea",
"input": "Problem: two 6 faced dice are thrown together . the probability that all the three show the same number on them is ? \nOptions: a ) 1 / 32 , b ) 1 / 6 , c ) 1 / 33 , d ) 1 / 38 , e ) 1 / 34",
"output": [
"b"
]
},
{
"id": "task1424-3652ddb0091c41edb283ea1d627fe425",
"input": "Problem: a jar contains only red , yellow , and orange marbles . if there are 3 red , 5 yellow , and 4 orange marbles , and 2 marbles are chosen from the jar at random without replacing any of them , what is the probability that 2 yellow , 1 red , and no orange marbles will be chosen ? \nOptions: a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 6 / 22",
"output": [
"e"
]
},
{
"id": "task1424-317354d3f85940cb9fa0efd2502c8c7f",
"input": "Problem: the membership of a committee consists of 3 english teachers , 4 mathematics teachers , and 2 social studies teachers . if 2 committee members are to be selected at random to write the committee ’ s report , what is the probability that the two members selected will both be maths teachers ? \nOptions: a ) 2 / 3 , b ) 1 / 3 , c ) 2 / 9 , d ) 1 / 24 , e ) 1 / 12",
"output": [
"e"
]
},
{
"id": "task1424-7c085e1bd3d843df9147edfbc0d9d727",
"input": "Problem: find the probability that a number selected from numbers 1 , 2 , 3 , . . . , 50 is a prime number , when each of the given numbers is equally likely to be selected ? \nOptions: a ) 10 / 50 , b ) 15 / 50 , c ) 8 / 50 , d ) 3 / 50 , e ) 7 / 50",
"output": [
"b"
]
},
{
"id": "task1424-d93e4364102b46258658121a6fff9da6",
"input": "Problem: the probability that a number selected at random from the first 100 natural numbers is a composite number is ? \nOptions: a ) 2 / 3 , b ) 3 / 5 , c ) 3 / 4 , d ) 3 / 2 , e ) 5 / 2",
"output": [
"d"
]
},
{
"id": "task1424-e63aed89c1274083bf66520fc44bb9da",
"input": "Problem: from a group of 3 women and 3 girls , 4 are to be randomly selected . what is the probability that equal numbers of women and girls will be selected ? \nOptions: a ) 3 / 5 , b ) 1 / 5 , c ) 2 / 5 , d ) 4 / 5 , e ) 1",
"output": [
"a"
]
},
{
"id": "task1424-19532ccb7fcf4089a28050e8f9a3b366",
"input": "Problem: how many positive integers less than 300 can be formed using the numbers 1 , 2 , 3 and 5 for the digits ? \nOptions: a ) 48 , b ) 52 , c ) 66 , d ) 68 , e ) 84",
"output": [
"b"
]
},
{
"id": "task1424-a04e7e3d0d1b472e8bc76f8f4c9f594d",
"input": "Problem: the maitre ' d at an expensive manhattan restaurant has noticed that 60 % of the couples order dessert and coffee . however , 20 % of the couples who order dessert do n ' t order coffee . what is the probability t that the next couple the maitre ' d seats will not order dessert ? \nOptions: a ) 20 % , b ) 25 % , c ) 40 % , d ) 60 % , e ) 75 %",
"output": [
"b"
]
},
{
"id": "task1424-5c9def544f5c43f5be67864b3167c912",
"input": "Problem: a bag contains 5 white marbles and 5 black marbles . if each of 5 girls and 5 boys randomly selects and keeps a marble , what is the probability that all of the girls select the same colored marble ? \nOptions: a ) 1 / 126 , b ) 1 / 120 , c ) 1 / 24 , d ) 4 / 25 , e ) 1 / 2",
"output": [
"a"
]
},
{
"id": "task1424-e1526b0842be4a429d24cc1c53cba7f2",
"input": "Problem: if two integers x , y ( x > y ) are selected from - 10 to 4 ( inclusive ) , how many possible cases are there ? \nOptions: a ) 150 , b ) 180 , c ) 190 , d ) 210 , e ) 105",
"output": [
"e"
]
},
{
"id": "task1424-39df279d15a4421eb633da1510283671",
"input": "Problem: 30 ladies and 60 gentlemen are present at a party . there are 23 couples among them . if a lady and a gentleman is selected at random , what is the probability that they will be a couple ? \nOptions: a ) 1 / 200 , b ) 1 / 100 , c ) 1 / 50 , d ) 1 / 40 , e ) 23 / 1800",
"output": [
"e"
]
},
{
"id": "task1424-d1ccbb255fe64aac994a1e691b4f6460",
"input": "Problem: there are 3 pairs of socks and 2 socks are worn from that such that the pair of socks worn are not of the same pair . what is the number of pair that can be formed . \nOptions: a ) 5 , b ) 1 , c ) 3 , d ) 6 , e ) 7",
"output": [
"d"
]
},
{
"id": "task1424-7a77815e244f403cbf142d62be7ab8e4",
"input": "Problem: in how many ways 5 boys and 5 girls can be seated in a row so that boys and girls are alternate ? \nOptions: a ) 28400 , b ) 28500 , c ) 28600 , d ) 28700 , e ) 28800",
"output": [
"e"
]
},
{
"id": "task1424-85708a712bbc44b392db5de34bc7a93e",
"input": "Problem: what is the probability that the sum of two dice will yield a 7 , and then when both are thrown again , their sum will again yield a 7 ? assume that each die has 6 sides with faces numbered 1 to 6 . \nOptions: a ) 1 / 144 , b ) 1 / 36 , c ) 1 / 12 , d ) 1 / 6 , e ) 1 / 3",
"output": [
"b"
]
},
{
"id": "task1424-ad13e1ed3cd343a984774fc4183665a8",
"input": "Problem: a string of 50 light bulbs is wired in such a way that if any individual light bulb fails , the entire string fails . if for each individual light bulb the probability of failing during time period t is 0.05 , what is the probability that the string of light bulbs will fail during the time period t ? \nOptions: a ) 0.05 , b ) ( 0.05 ) ^ 50 , c ) 1 - ( 0.96 ) ^ 50 , d ) 1 - ( 0.95 ) ^ 50 , e ) ( 0.95 ) ^ 50",
"output": [
"d"
]
},
{
"id": "task1424-df9f13e9f34b4b96a9831649e066b6a9",
"input": "Problem: in a throw of dice what is the probability of ge æ « ng number greater than 2 \nOptions: a ) 1 / 2 , b ) 2 / 3 , c ) 1 / 5 , d ) 1 / 6 , e ) none of these",
"output": [
"b"
]
},
{
"id": "task1424-cc9543a837cf405ca08e76af5cc091a1",
"input": "Problem: in a throw of dice what is the probability of ge æ « ing number greater than 2 \nOptions: a ) 2 / 3 , b ) 1 / 3 , c ) 1 / 5 , d ) 1 / 6 , e ) none of these",
"output": [
"a"
]
},
{
"id": "task1424-85e1798c05fd4e41b039ebec9f6c517c",
"input": "Problem: in how many ways 6 boys and 6 girls can be seated in a row so that boys and girls are alternate ? \nOptions: a ) 1063800 , b ) 1083600 , c ) 1036800 , d ) 1053800 , e ) 1073600",
"output": [
"c"
]
},
{
"id": "task1424-1ba57ffb4b3140e5b96ac82559b2ad22",
"input": "Problem: a certain junior class has 1000 students and a certain senior class has 800 students . among these students , there are 40 siblings pairs each consisting of 1 junior and 1 senior . if 1 student is to be selected at random from each class , what is the probability that the 2 students selected will be a sibling pair ? \nOptions: a ) 3 / 40000 , b ) 1 / 3600 , c ) 1 / 20000 , d ) 1 / 60 , e ) 1 / 15",
"output": [
"c"
]
},
{
"id": "task1424-b6f16634af504b3683b2fce4cedb8712",
"input": "Problem: if two integers x , y ( x > y ) are selected from - 10 to 1 ( inclusive ) , how many possible cases are there ? \nOptions: a ) 150 , b ) 66 , c ) 190 , d ) 210 , e ) 240",
"output": [
"b"
]
},
{
"id": "task1424-5581c231dd9b40f1abeafaf9e5cf8e98",
"input": "Problem: what is the probability of getting a sum of 8 or 14 when rolling 3 dice simultaneously ? \nOptions: a ) 1 / 6 , b ) 1 / 4 , c ) 1 / 2 , d ) 21 / 216 , e ) 32 / 216",
"output": [
"a"
]
},
{
"id": "task1424-f5738df0d29d4eb58ae012ac0af48314",
"input": "Problem: from a group of 5 boys and 5 girls , 6 children are to be randomly selected . what is the probability that 3 boys and 3 girls will be selected ? \nOptions: a ) 4 / 15 , b ) 6 / 17 , c ) 8 / 19 , d ) 10 / 21 , e ) 12 / 23",
"output": [
"d"
]
},
{
"id": "task1424-209297b4e0bb456f93444ede52ebb969",
"input": "Problem: a box contains 21 electric bulbs , out of which 4 are defective . two bulbs are chosen at random from this box . the probability that at least one of these is defective is \nOptions: a ) 4 / 19 , b ) 7 / 19 , c ) 12 / 19 , d ) 21 / 95 , e ) 31 / 88",
"output": [
"e"
]
},
{
"id": "task1424-cce481d78a6c43df821c716ed3d5d5c4",
"input": "Problem: a coin is tossed six times . what is the probability that there is at the least one tail ? \nOptions: a ) 63 / 64 , b ) 31 / 37 , c ) 31 / 18 , d ) 31 / 10 , e ) 31 / 19",
"output": [
"a"
]
},
{
"id": "task1424-810619f03e0f4d639c92a7c88f2b7423",
"input": "Problem: the maitre ' d at an expensive manhattan restaurant has noticed that 60 % of the couples order dessert and coffee . however , 20 % of the couples who order dessert do n ' t order coffee . what is the probability w that the next couple the maitre ' d seats will not order dessert ? \nOptions: a ) 20 % , b ) 25 % , c ) 40 % , d ) 60 % , e ) 75 %",
"output": [
"b"
]
},
{
"id": "task1424-1e8ae7d47e9f483b94a5787a74c69b8c",
"input": "Problem: a bag consists of 30 marbles , of which 5 are blue , 9 are red , and the remainder are white . if lisa is to select a marble from the bag at random , what is the probability that the marble will be red or white ? \nOptions: a ) 5 / 6 , b ) 2 / 4 , c ) 1 / 4 , d ) 1 / 8 , e ) 1 / 16",
"output": [
"a"
]
},
{
"id": "task1424-2ce84024b05447eabaffbf64668f03c3",
"input": "Problem: in how many ways 4 boys and 3 girls can be seated in a row so that they are alternate . \nOptions: a ) 144 , b ) 288 , c ) 12 , d ) 256 , e ) none",
"output": [
"a"
]
},
{
"id": "task1424-f1a4c2cf520042d0aa2bb134f6c6c2b9",
"input": "Problem: how many different ways can 2 students be seated in a row of 5 desks , so that there is always at least one empty desk between the students ? \nOptions: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 12",
"output": [
"e"
]
},
{
"id": "task1424-e197d8fa66a748408d60aec28b2d6878",
"input": "Problem: there are 5 red shoes & 4 green shoes . if two of red shoes are drawn what is the probability of getting red shoes \nOptions: a ) 1 / 18 , b ) 1 / 14 , c ) 5 / 18 , d ) 1 / 15 , e ) 1 / 16",
"output": [
"c"
]
},
{
"id": "task1424-7d90ea03281b47d88db1fceff7625069",
"input": "Problem: in a certain animal population , for each of the first 3 months of life , the probability that an animal will die during that month is 1 / 10 . for a group of 400 newborn members of the population , approximately how many would be expected to survive the first 3 months of life ? \nOptions: a ) 240 , b ) 246 , c ) 252 , d ) 292 , e ) 298",
"output": [
"d"
]
},
{
"id": "task1424-22db9b68d6fc4d3eb6c566d08600d2cb",
"input": "Problem: when 3 fair coins are tossed together , what is the probability of getting 2 tails ? \nOptions: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 3 / 4 , e ) 2 / 3",
"output": [
"a"
]
},
{
"id": "task1424-a42f05ad6e8a4d43955bda9ed3b36432",
"input": "Problem: if g is to be chosen at random from the set { 5,8 , 7,1 } and k is to be chosen at random from the set { 14 , 8,3 } , what is the probability that gk will be even ? \nOptions: a ) 1 , b ) 5 , c ) 8 , d ) 4 , e ) 3",
"output": [
"a"
]
},
{
"id": "task1424-641aea8125ec4e88b7f846657f59ac30",
"input": "Problem: a box contains 20 electric bulbs , out of which 4 are defective . two bulbs are chosen at random form this box . the probability that at least one of these is defective is : \nOptions: a ) 8 / 19 , b ) 7 / 19 , c ) 10 / 19 , d ) 20 / 19 , e ) 22 / 19",
"output": [
"b"
]
},
{
"id": "task1424-61d19741f48a4ee5a79996724101408f",
"input": "Problem: if 4 people are selected from a group of 8 married couples , what is the probability that none of them would be married to each other ? \nOptions: a ) 1 / 33 , b ) 2 / 33 , c ) 8 / 13 , d ) 16 / 33 , e ) 11 / 12",
"output": [
"c"
]
},
{
"id": "task1424-041960249d804da69d3d6dbaed7b18e9",
"input": "Problem: 3.00001 unbiased coins are tossed . what is the probability of getting 2 tails ? \nOptions: a ) 3 / 4 , b ) 1 / 4 , c ) 3 / 8 , d ) 7 / 8 , e ) 1 / 8",
"output": [
"c"
]
},
{
"id": "task1424-4d1d76c661ed469eb712dfe11465a1ff",
"input": "Problem: in how many ways 4 boys and 1 girls can be seated in a row so that they are alternate . \nOptions: a ) 144 , b ) 288 , c ) 24 , d ) 256 , e ) none",
"output": [
"c"
]
},
{
"id": "task1424-a21c987380f7409baebd287a620e9108",
"input": "Problem: wink , inc . follows a certain procedure that requires two tasks to be finished independently in order for a job to be done . on any given day , there is a 3 / 8 probability that task 1 will be completed on time , and a 3 / 5 probability that task 2 will be completed on time . on a certain day , what is the probability that task 1 will be completed on time , but task 2 will not ? \nOptions: a ) 1 / 20 , b ) 3 / 40 , c ) 13 / 40 , d ) 3 / 20 , e ) 13 / 22",
"output": [
"d"
]
},
{
"id": "task1424-7c2a2c03f39f40c39332809959bfe17a",
"input": "Problem: 5 letters have to be put in 5 different envelopes numbered 1 through 5 such that each of the letters go into only 1 envelope . the letter is said to be put in correct position if for example letter 1 goes into envelope 1 . now what is the probability that all letters be put into wrong envelopes ? \nOptions: a ) 1 / 3 , b ) 2 / 3 , c ) 11 / 120 , d ) 11 / 30 , e ) 76 / 120",
"output": [
"d"
]
},
{
"id": "task1424-5458b7c1100b46ef872967df04dcd93f",
"input": "Problem: there is a 50 % chance jen will visit chile this year , while there is a 25 % chance that she will visit madagascar this year . what is the probability that jen will visit either chile or madagascar this year , but not both ? [ / b ] \nOptions: a ) 25 % , b ) 50 % , c ) 62.5 % , d ) 63.5 % , e ) 75 %",
"output": [
"b"
]
},
{
"id": "task1424-c6f014f785da4c5a8a788ab659f6bca4",
"input": "Problem: kim has 5 pairs of shoes ; each pair is a different color . if kim randomly selects 2 shoes without replacement from the 10 shoes , what is the probability that she will select 2 shoes of the same color ? \nOptions: a ) 2 / 5 , b ) 1 / 5 , c ) 1 / 9 , d ) 1 / 10 , e ) 1 / 25",
"output": [
"c"
]
},
{
"id": "task1424-d6093709a1354fe58bd1cda94a07d48c",
"input": "Problem: a fair coin is tossed 11 times . what is the probability of getting more heads than tails in 11 tosses ? \nOptions: a ) 1 / 2 , b ) 63 / 128 , c ) 4 / 7 , d ) 61 / 256 , e ) 63 / 64",
"output": [
"a"
]
},
{
"id": "task1424-d2f81af99d0c4cb1a695c81991e51801",
"input": "Problem: three unbiased coins are tossed . what is the probability of getting at least 2 tails ? \nOptions: a ) 0.75 , b ) 0.5 , c ) 0.25 , d ) 0.2 , e ) 0.3",
"output": [
"b"
]
},
{
"id": "task1424-75e6b0fd4e4a44a18871889924f5bb4f",
"input": "Problem: a meeting has to be conducted with 4 managers . find the number of ways in which the managers be selected from among 7 managers , if 2 managers will not attend the meeting together ? \nOptions: a ) 25 , b ) 20 , c ) 35 , d ) 36 , e ) 38",
"output": [
"a"
]
},
{
"id": "task1424-3bba787dc8e84e7e9c542ea9c2a5053f",
"input": "Problem: bill and jane play a simple game involving two fair dice , each of which has 6 sides numbered from 1 to 6 ( with an equal chance of landing on any side ) . bill rolls the dice and his score is the total of the two dice . jane then rolls the dice and her score is the total of her two dice . if jane ’ s score is higher than bill ’ s , she wins the game . what is the probability the jane will win the game ? \nOptions: a ) 15 / 36 , b ) 175 / 432 , c ) 575 / 1296 , d ) 583 / 1296 , e ) 1 / 2",
"output": [
"c"
]
},
{
"id": "task1424-67ae5c04c8fa4ede80ef3fe7d501d10b",
"input": "Problem: a jar contains 3 black , 3 white and 1 green balls . if you pick two balls at the same time , what ' s the probability that one ball is black and one is white ? \nOptions: a ) 2 / 7 , b ) 5 / 7 , c ) 4 / 7 , d ) 3 / 7 , e ) 1 / 2",
"output": [
"d"
]
},
{
"id": "task1424-d3c13e0315fa46e8bf8a15cb361d73e8",
"input": "Problem: a meeting has to be conducted with 5 managers . find the number of ways in which the managers be selected from among 8 managers , if 2 managers will not attend the meeting together ? \nOptions: a ) 40 , b ) 36 , c ) 42 , d ) 45 , e ) 47",
"output": [
"b"
]
},
{
"id": "task1424-204c512f7bd0489d852a1828a7439b61",
"input": "Problem: in lottery , there are 10 prizes and 25 blanks . a lottery is drawn at random . what is the probability of getting a prize ? \nOptions: a ) 1 / 7 , b ) 2 / 7 , c ) 3 / 7 , d ) 4 / 7 , e ) 1",
"output": [
"b"
]
},
{
"id": "task1424-05c89ada393a457eb868cc4757a73bbd",
"input": "Problem: how many different ways can 2 students be seated in a row of 3 desks , so that there is always at least one empty desk between the students ? \nOptions: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 12",
"output": [
"a"
]
},
{
"id": "task1424-c1f6f47acc9847f798e8d0bc33f589f0",
"input": "Problem: john and peter are among the 9 players a volleyball coach can choose from to field a 6 - player team . if all 6 players are chosen at random , what is the probability of choosing a team that includes john and peter ? \nOptions: a ) 3 / 10 , b ) 4 / 11 , c ) 5 / 12 , d ) 6 / 13 , e ) 7 / 15",
"output": [
"c"
]
},
{
"id": "task1424-0d7d7e503c15484db79435744bcf4f73",
"input": "Problem: three unbiased coins are tossed . what is the probability of getting 1 heads and 1 tail ? \nOptions: a ) 3 / 4 , b ) 1 / 4 , c ) 3 / 8 , d ) 7 / 8 , e ) 1 / 8",
"output": [
"b"
]
},
{
"id": "task1424-a0925994d6c64719a55f32bfbcb0ee95",
"input": "Problem: two mba admissions committees are to be formed randomly from 6 second year mbas with 3 members each . what is the probability q that jane will be on the same committee as albert ? \nOptions: a ) 12 % , b ) 20 % , c ) 33 % , d ) 40 % , e ) 50 %",
"output": [
"d"
]
},
{
"id": "task1424-aa439b8aadc84306988dfcc8a943f143",
"input": "Problem: on a ranch , a rancher can place a loop of rope , called a lasso , once in every 2 throws around a cow ’ s neck . what is the probability that the rancher will be able to place a lasso around a cow ’ s neck at least once in 4 attempts ? \nOptions: a ) 3 / 4 , b ) 5 / 8 , c ) 7 / 8 , d ) 11 / 16 , e ) 15 / 16",
"output": [
"e"
]
},
{
"id": "task1424-bdb66537af2d42b79e200e6788e92edb",
"input": "Problem: find the probability that a number selected from numbers 1 , 2 , 3 , . . . , 20 is a prime number , when each of the given numbers is equally likely to be selected ? \nOptions: a ) 10 / 20 , b ) 1 / 20 , c ) 8 / 20 , d ) 3 / 20 , e ) 7 / 20",
"output": [
"c"
]
},
{
"id": "task1424-7f6568c3eddf4984871371b243604db8",
"input": "Problem: two letters from the word barkhint are selected at random . what is the probability that at least one of the selected letters is a consonant ? \nOptions: a ) 30 / 28 , b ) 40 / 28 , c ) 25 / 28 , d ) 27 / 28 , e ) 32 / 28",
"output": [
"d"
]
},
{
"id": "task1424-76724125213c492ab32b9622b14b7916",
"input": "Problem: a certain junior class has 3000 students and a certain senior class has 800 students . among these students , there are 60 siblings pairs each consisting of 1 junior and 1 senior . if 1 student is to be selected at random from each class , what is the probability that the 2 students selected will be a sibling pair ? \nOptions: a ) 1 / 40000 , b ) 1 / 3600 , c ) 9 / 2000 , d ) 1 / 60 , e ) 1 / 15",
"output": [
"a"
]
},
{
"id": "task1424-157265871d2544b5b2cdcf4b8b1e460d",
"input": "Problem: the maitre ' d at an expensive manhattan restaurant has noticed that 60 % of the couples order dessert and coffee . however , 20 % of the couples who order dessert do n ' t order coffee . what is the probability q that the next couple the maitre ' d seats will not order dessert ? \nOptions: a ) 20 % , b ) 25 % , c ) 40 % , d ) 60 % , e ) 75 %",
"output": [
"b"
]
},
{
"id": "task1424-3a28414fef334b2f8d928dcd6b10d41e",
"input": "Problem: there are 3 red shoes & 7 green shoes . if two of red shoes are drawn what is the probability of getting red shoes \nOptions: a ) 1 / 13 , b ) 1 / 14 , c ) 1 / 12 , d ) 1 / 15 , e ) 1 / 16",
"output": [
"d"
]
},
{
"id": "task1424-ae8e76d783434e9c9cfd2215239e06c1",
"input": "Problem: a bag consists of 60 marbles , of which 5 are blue , 9 are red , and the remainder are white . if lisa is to select a marble from the bag at random , what is the probability that the marble will be red or white ? \nOptions: a ) 11 / 12 , b ) 2 / 4 , c ) 1 / 4 , d ) 1 / 8 , e ) 1 / 16",
"output": [
"a"
]
},
{
"id": "task1424-d0334138bdab4a7181e8cf50d10dbf6c",
"input": "Problem: if a coin is flipped , the probability that the coin will land tails is 1 / 2 . if the coin is flipped 5 times , what is the probability that it will land tails up on the first 2 flips and not on the last 3 flips ? \nOptions: a ) 3 / 5 , b ) 1 / 32 , c ) 1 / 5 , d ) 1 / 4 , e ) 1 / 2",
"output": [
"b"
]
},
{
"id": "task1424-1531e5fff0ed4e85b63c347a6c55a40b",
"input": "Problem: in how many ways can 7 boys be seated in a circular order ? \nOptions: a ) 110 , b ) 230 , c ) 720 , d ) 420 , e ) 680",
"output": [
"c"
]
},
{
"id": "task1424-d2c7d24bee40469c929cc7a8b4bc71cc",
"input": "Problem: there is a 75 % chance that tigers will not win at all during the whole season . there is a 25 % chance that germany will not play at all in the whole season . what is the greatest possible probability that the tigers will win and germany will play during the season ? \nOptions: a ) 55 % , b ) 60 % , c ) 70 % , d ) 75 % , e ) 80 %",
"output": [
"d"
]
},
{
"id": "task1424-740a89d5bd574664b1353551896d4ec7",
"input": "Problem: the maitre ' d at an expensive manhattan restaurant has noticed that 60 % of the couples order dessert and coffee . however , 20 % of the couples who order dessert do n ' t order coffee . what is the probability y that the next couple the maitre ' d seats will not order dessert ? \nOptions: a ) 20 % , b ) 25 % , c ) 40 % , d ) 60 % , e ) 75 %",
"output": [
"b"
]
},
{
"id": "task1424-099a7ac6364147b7896c6f51c7fb267b",
"input": "Problem: in how many ways can 21 books on english and 19 books on french be placed in a row on a shelf so that two books on french may not be together ? \nOptions: a ) 3990 , b ) 1540 , c ) 1995 , d ) 3672 , e ) none of these",
"output": [
"b"
]
},
{
"id": "task1424-fdada8bee02746f98fe663c88755adef",
"input": "Problem: from a pack of 52 cards , two cards are drawn at random together at random what is the probability of both the cards being kings ? \nOptions: a ) 1 / 221 , b ) 8 / 221 , c ) 4 / 589 , d ) 4 / 587 , e ) 7 / 654",
"output": [
"a"
]
},
{
"id": "task1424-80e399682ea64640b86b0dd24c6281cb",
"input": "Problem: two mba admissions committees are to be formed randomly from 6 second year mbas with 3 members each . what is the probability w that jane will be on the same committee as albert ? \nOptions: a ) 12 % , b ) 20 % , c ) 33 % , d ) 40 % , e ) 50 %",
"output": [
"d"
]
},
{
"id": "task1424-8fc6623e396343f89c8736f5564f7e0c",
"input": "Problem: in a certain animal population , for each of the first 3 months of life , the probability that an animal will die during that month is 1 / 10 . for a group of 600 newborn members of the population , approximately how many would be expected to survive the first 3 months of life ? \nOptions: a ) 438 , b ) 446 , c ) 452 , d ) 462 , e ) 470",
"output": [
"a"
]
},
{
"id": "task1424-9623d9752b934a51ac852f198fba719c",
"input": "Problem: a fair coin is tossed 5 times . what is the probability that it lands heads up at least twice ? \nOptions: a ) 1 / 16 , b ) 5 / 16 , c ) 2 / 5 , d ) 13 / 16 , e ) 27 / 32",
"output": [
"d"
]
},
{
"id": "task1424-51d6963a696f4252ae535fd7a311c162",
"input": "Problem: kim has 6 pairs of shoes ; each pair is a different color . if kim randomly selects 2 shoes without replacement from the 12 shoes , what is the probability that she will select 2 shoes of the same color ? \nOptions: a ) 2 / 5 , b ) 1 / 5 , c ) 1 / 9 , d ) 1 / 11 , e ) 1 / 25",
"output": [
"d"
]
},
{
"id": "task1424-dd628d26b74f42989062cf833a70abb3",
"input": "Problem: jane and thomas are among the 8 people from which a committee of 3 people is to be selected . how many different possible committees of 3 people can be selected from these 8 people if at least one of either jane or thomas is to be selected ? \nOptions: a ) 24 , b ) 28 , c ) 32 , d ) 36 , e ) 40",
"output": [
"d"
]
},
{
"id": "task1424-d88ef73d253e4e94a1d6748ac4a101a2",
"input": "Problem: a card is drawn from a pack of 52 cards . the probability of getting a queen of club or a king of heart is \nOptions: a ) 1 / 13 , b ) 2 / 13 , c ) 1 / 26 , d ) 1 / 52 , e ) 1 / 23",
"output": [
"c"
]
},
{
"id": "task1424-6e4936c0cca04f649a685834e9da9147",
"input": "Problem: three 6 faced dice are thrown together . the probability that no two dice show the same number on them is \nOptions: a ) 5 / 0 , b ) 5 / 9 , c ) 5 / 1 , d ) 5 / 3 , e ) 5 / 6",
"output": [
"b"
]
},
{
"id": "task1424-ae671b4feaaf48a1a371792e1d6cd69c",
"input": "Problem: two mba admissions committees are to be formed randomly from 6 second year mbas with 3 members each . what is the probability r that jane will be on the same committee as albert ? \nOptions: a ) 12 % , b ) 20 % , c ) 33 % , d ) 40 % , e ) 50 %",
"output": [
"d"
]
},
{
"id": "task1424-e36e66d6a6e245399434fcbdfa11e8ea",
"input": "Problem: an unbaised coin is tossed until it shows up the same face in 2 consicative throws wat is the probability that the no of tosses is not more than 4 . \nOptions: a ) 3 / 4 , b ) 1 / 4 , c ) 7 / 8 , d ) 1 / 8 , e ) 6 / 8",
"output": [
"c"
]
},
{
"id": "task1424-8ff85c5142cb4baab9d23857162911bf",
"input": "Problem: what is the probability of randomly selecting one of the shortest diagonals from all the diagonals of a regular 9 - sided polygon ) ? \nOptions: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 6 , e ) 1 / 9",
"output": [
"b"
]
},
{
"id": "task1424-f9fab0f903784fe5a42a0aca13d8d6d6",
"input": "Problem: from a group of 4 boys and 4 girls , 6 children are to be randomly selected . what is the probability that 3 boys and 3 girls will be selected ? \nOptions: a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 5 , d ) 4 / 7 , e ) 5 / 9",
"output": [
"d"
]
},
{
"id": "task1424-10968d3b8cfa4e70b4bdea40ddeaf814",
"input": "Problem: how many cubes of 5 cm edge can be cut out of a cube of 20 cm edge \nOptions: a ) 36 , b ) 64 , c ) 216 , d ) 484 , e ) none of these",
"output": [
"b"
]
},
{
"id": "task1424-e2e00d8ca0f248af8bf19f8b2bf3ae7d",
"input": "Problem: the probability is 1 / 2 that a certain coin turns up heads on any given toss . if the coin is tossed 6 times , what is the probability that the coin turns up tails on at least one of the tosses ? \nOptions: a ) 15 / 16 , b ) 21 / 32 , c ) 31 / 32 , d ) 63 / 64 , e ) 51 / 64",
"output": [
"d"
]
},
{
"id": "task1424-2d075fe4a6a248c68c8eeb927a094e3f",
"input": "Problem: if x is to be chosen at random from the set { 1 , 2 , 3 , 4 } and y is to be chosen at random from the set { 5 , 6 } , what is the probability that xy will be even ? \nOptions: a ) 1 / 6 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 6",
"output": [
"b"
]
},
{
"id": "task1424-9bd6b1c63f374e84a79c060586aaf7ed",
"input": "Problem: a bag contains 6 black and 7 white balls . one ball is drawn at random . what is the probability that the ball drawn is white ? \nOptions: a ) 4 , b ) 4 / 3 , c ) 4 / 5 , d ) 4 / 9 , e ) 7 / 13",
"output": [
"e"
]
},
{
"id": "task1424-602d2b96fdec4102b7cfc39b276fb565",
"input": "Problem: three unbiased coins are tossed . what is the probability of getting all tails ? \nOptions: a ) 7 / 8 , b ) 1 / 2 , c ) 3 / 8 , d ) 1 / 4 , e ) 1 / 8",
"output": [
"e"
]
},
{
"id": "task1424-d99118a031f24bc6ad0da375f262659f",
"input": "Problem: what is the probability that jamie and tom will get selected for a job they both applied for in a company , given that their chances of getting selected is 2 / 3 and 5 / 7 respectively ? \nOptions: a ) 13 / 25 , b ) 2 / 5 , c ) 9 / 20 , d ) 11 / 20 , e ) 10 / 21",
"output": [
"e"
]
},
{
"id": "task1424-a8d2ba87e6f74c0f8b3351dfd76b3904",
"input": "Problem: a jar contains 4 black and 3 white balls . if you pick two balls at the same time , what ' s the probability that one ball is black and one is white ? \nOptions: a ) 2 / 7 , b ) 5 / 7 , c ) 4 / 7 , d ) 3 / 7 , e ) 1 / 2",
"output": [
"c"
]
},
{
"id": "task1424-434ba25a2e9d413d85ecabebbf0fd0a2",
"input": "Problem: how many positive integers less than 300 can be formed using the numbers 1 , 2 , 3 a for the digits ? \nOptions: a ) 30 , b ) 52 , c ) 66 , d ) 68 , e ) 84",
"output": [
"a"
]
},
{
"id": "task1424-e2d5906adedc42488f1646e301ff6a39",
"input": "Problem: from a pack of 52 cards , 1 card is drawn at random . what is the probability that a king is drawn ? \nOptions: a ) 1 / 4 , b ) 4 / 13 , c ) 1 / 13 , d ) 3 / 26 , e ) 7 / 52",
"output": [
"c"
]
},
{
"id": "task1424-26c4fa315b604daaa44f53517ef07f6c",
"input": "Problem: in a throw of a coin find the probability of getting a head ? \nOptions: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 2 / 3 , e ) 2 / 5",
"output": [
"a"
]
},
{
"id": "task1424-6fe84659b67b4618a2c1c41912f7fd7e",
"input": "Problem: find the probability that a leap year selected at random will have 53 mondays \nOptions: a ) 6 / 7 , b ) 5 / 7 , c ) 4 / 7 , d ) 3 / 7 , e ) 2 / 7",
"output": [
"e"
]
},
{
"id": "task1424-a9375403482841188915f8209ec651ad",
"input": "Problem: the probability that event a occurs is 0.4 , and the probability that event b occurs is 0.45 . if the probability that either event a or event b occurs is 0.6 , what is the probability that event b and event b will occur ? \nOptions: a ) 0.25 , b ) 0.15 , c ) 0.45 , d ) 0.5 , e ) 0.55",
"output": [
"a"
]
},
{
"id": "task1424-ca6bc4f700204e17b0e23310101a2368",
"input": "Problem: a coin is tossed 6 times . what is the probability of getting exactly 5 heads ? \nOptions: a ) 3 / 8 , b ) 3 / 16 , c ) 5 / 16 , d ) 3 / 32 , e ) 7 / 64",
"output": [
"d"
]
},
{
"id": "task1424-c44a05f691e24809806994c740213c9c",
"input": "Problem: in a certain animal population , for each of the first 3 months of life , the probability that an animal will die during that month is 1 / 6 . for a group of 200 newborn members of the population , approximately how many would be expected to survive the first 3 months of life ? \nOptions: a ) 116 , b ) 146 , c ) 152 , d ) 162 , e ) 170",
"output": [
"a"
]
},
{
"id": "task1424-48cdf9774cbb4c3783e0a8fd67d3b7b7",
"input": "Problem: three unbiased coins are tossed . what is the probability of getting at most 2 heads ? \nOptions: a ) 7 / 8 , b ) 5 / 8 , c ) 3 / 8 , d ) 7 / 5 , e ) 3 / 5",
"output": [
"a"
]
},
{
"id": "task1424-d0ebd7835e0b4c7788174fb096cc26c7",
"input": "Problem: there is a 20 % chance sandy will visit china this year , while there is a 70 % chance that she will visit malaysia this year . what is the probability that sandy will visit either china or malaysia this year , but not both ? \nOptions: a ) 44 % , b ) 48 % , c ) 54 % , d ) 62 % , e ) 70 %",
"output": [
"d"
]
},
{
"id": "task1424-b24887bb59d4401cae647530aa1a42ee",
"input": "Problem: 4 dice are thrown simultaneously on the board . find the probability which show the same face ? \nOptions: a ) 2 / 113 , b ) 3 / 117 , c ) 1 / 216 , d ) 3 / 111 , e ) 4 / 121",
"output": [
"c"
]
},
{
"id": "task1424-88e5e6163f9448b1b695cb9a3dafc98f",
"input": "Problem: if a certain coin is flipped , the probability that the coin will land heads is 1 / 2 . if the coin is flipped 5 times , what is the probability that it will land heads up on the first flip but not on the last 4 flips ? \nOptions: a ) 1 / 4 , b ) 1 / 8 , c ) 1 / 16 , d ) 1 / 32 , e ) 1 / 64",
"output": [
"d"
]
},
{
"id": "task1424-9c1ca1fc9a5a4f12b5ed9132a002df26",
"input": "Problem: there are 22 students in a class . in how many different ways can a committee of 3 students be formed ? \nOptions: a ) 1180 , b ) 1320 , c ) 1540 , d ) 1760 , e ) 1920",
"output": [
"c"
]
},
{
"id": "task1424-391f981c00b0482cb3402339abfca78b",
"input": "Problem: a box contains 100 balls , numbered from 1 to 100 . if 3 balls are selected at random and with replacement from the box . if the 3 numbers on the balls selected contain two odd and one even . what is the probability l that the first ball picked up is odd numbered ? \nOptions: a ) 0 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 1",
"output": [
"d"
]
},
{
"id": "task1424-c5c138d4350546dbae0d3a737fae5156",
"input": "Problem: there is a 30 % chance jen will visit chile this year , while there is a 50 % chance that she will visit madagascar this year . what is the probability that jen will visit either chile or madagascar this year , but not both ? \nOptions: a ) 25.0 % , b ) 37.5 % , c ) 50.0 % , d ) 62.5 % , e ) 75 %",
"output": [
"c"
]
},
{
"id": "task1424-8c6980e4f5574d8ba4cb231b70835638",
"input": "Problem: 4 dice are thrown simultaneously on the board . find the probability show the same face ? \nOptions: a ) 2 / 113 , b ) 1 / 215 , c ) 1 / 216 , d ) 3 / 113 , e ) 4 / 113",
"output": [
"c"
]
},
{
"id": "task1424-e3cb70aecd224e85bd6e0aa0d6c9a9dd",
"input": "Problem: the probability that a number selected at random from the first 50 natural numbers is a composite number is \nOptions: a ) 17 / 26 , b ) 17 / 25 , c ) 17 / 20 , d ) 17 / 22 , e ) 17 / 21",
"output": [
"b"
]
},
{
"id": "task1424-abb1ea3f7a6043528f20437fa87f979e",
"input": "Problem: a box contains 24 electric bulbs , out of which 4 are defective . two bulbs are chosen at random from this box . the probability that at least one of these is defective is \nOptions: a ) 4 / 19 , b ) 7 / 19 , c ) 12 / 19 , d ) 24 / 77 , e ) none",
"output": [
"d"
]
},
{
"id": "task1424-157a6d493cdd4ade8ea0fdbef131e8f1",
"input": "Problem: what is the probability of having 53 fridays in an ordinary year \nOptions: a ) 1 / 5 , b ) 1 / 6 , c ) 1 / 7 , d ) 1 / 8 , e ) 1 / 9",
"output": [
"c"
]
},
{
"id": "task1424-599d699da02941eaa7f3b909ad8479e2",
"input": "Problem: a , b , c , d , e sitting in a row what is the probability that a & b sitting adjacent . \nOptions: a ) 1 / 5 , b ) 2 / 5 , c ) 3 / 5 , d ) 4 / 5 , e ) 6 / 5",
"output": [
"b"
]
},
{
"id": "task1424-250414edb37e446b9cde60113e186f08",
"input": "Problem: what is the probability of getting sum of 10 on rolling three dices ? \nOptions: a ) 28 / 216 , b ) 27 / 216 , c ) 29 / 216 , d ) 26 / 216 , e ) 25 / 216",
"output": [
"b"
]
},
{
"id": "task1424-8258f30519a34cfbb1b183cc7ae70046",
"input": "Problem: a bag contains 20 red jellybeans and 20 blue jellybeans . if 3 jellybeans are removed one at a time , at random and are not replaced , what is the probability that all 3 jellybeans removed from the bag are blue ? \nOptions: a ) 9 / 100 , b ) 2 / 19 , c ) 1 / 8 , d ) 3 / 20 , e ) 3 / 10",
"output": [
"d"
]
},
{
"id": "task1424-72e0aa5ed8f74b1a9185e821952a0f12",
"input": "Problem: what is the probability that the sum of two dice will yield a 4 , and then when both are thrown again , their sum will again yield a 4 ? assume that each die has 3 sides with faces numbered 1 to 3 . \nOptions: a ) 1 / 144 , b ) 1 / 36 , c ) 1 / 9 , d ) 1 / 6 , e ) 1 / 3",
"output": [
"c"
]
},
{
"id": "task1424-3347ee297a064dfaab403a892cfc9888",
"input": "Problem: what is the probability of randomly selecting an arrangement of the letters of the word ` ` mediterranean ' ' in which the first letter is e and the last letter is r ? \nOptions: a ) 1 / 13 , b ) 1 / 20 , c ) 1 / 26 , d ) 1 / 50 , e ) 1 / 100",
"output": [
"c"
]
},
{
"id": "task1424-a4b18b525c214a9c8075db2afa810471",
"input": "Problem: three unbiased coins are tossed . what is the probability of getting at most two heads ? \nOptions: a ) 3 / 4 , b ) 1 / 4 , c ) 3 / 8 , d ) 7 / 8 , e ) none of these",
"output": [
"d"
]
},
{
"id": "task1424-b6bc4032368e4f83b1f8c037c6ab0559",
"input": "Problem: in a garden , there are yellow and green flowers which are straight and curved . if the probability of picking a green flower is 1 / 6 and picking a straight flower is 1 / 2 , then what is the probability of picking a flower which is yellow and straight \nOptions: a ) 1 / 7 , b ) 1 / 8 , c ) 1 / 4 , d ) 3 / 7 , e ) 7 / 8",
"output": [
"d"
]
},
{
"id": "task1424-545803118dbe4a43bc472d1797fe3168",
"input": "Problem: what is the probability of drawing a ` ` queen ' ' from a deck of 52 cards ? \nOptions: a ) 2 / 7 , b ) 1 / 13 , c ) 3 / 5 , d ) 2 / 8 , e ) 1 / 7",
"output": [
"b"
]
},
{
"id": "task1424-afeeea33326b4f6faf35e34c93379e3f",
"input": "Problem: three 6 faced dice are thrown together . the probability that all the three show the same number on them is - . \nOptions: a ) 1 / 36 , b ) 1 / 216 , c ) 1 / 48 , d ) 1 / 55 , e ) 1 / 90",
"output": [
"a"
]
},
{
"id": "task1424-94a01d8e267646be8c1d40b58b5087f2",
"input": "Problem: a gardener is going to plant 2 red rosebushes and 2 white rosebushes . if the gardener is to select each of the bushes at random , one at a time , and plant them in a row , what is the probability that the 2 rosebushes in the middle of the row will be the red rosebushes ? \nOptions: a ) 1 / 12 , b ) 1 / 6 , c ) 1 / 5 , d ) 1 / 3 , e ) ½",
"output": [
"b"
]
},
{
"id": "task1424-056ca5792f584a238c5fa3cc4bc6a843",
"input": "Problem: if you roll one fair 6 - sided die , what is the probability that the number is even or less than 3 ? \nOptions: a ) 2 / 3 , b ) 1 / 2 , c ) 3 / 4 , d ) 5 / 6 , e ) 1 / 3",
"output": [
"a"
]
},
{
"id": "task1424-6c84f1f5e9594352932a06c9ea92c335",
"input": "Problem: if you keep rolling a pair of dice together till a sum of 5 or 7 is obtained , then what is the probability that a sum of 5 comes before a sum of 7 ? \nOptions: a ) 5 / 5 , b ) 4 / 5 , c ) 3 / 5 , d ) 2 / 5 , e ) 1 / 5",
"output": [
"d"
]
},
{
"id": "task1424-7a20a36b9f174b27bd642f66a1638185",
"input": "Problem: if 4 consecutive letters are selected at random from the english alphabet , then the probability that one of the letters is a vowel is ? \nOptions: a ) 13 / 23 , b ) 16 / 23 , c ) 11 / 23 , d ) 17 / 23 , e ) 18 / 23",
"output": [
"d"
]
},
{
"id": "task1424-db8ac29734e7474c9baf225faa8494b0",
"input": "Problem: a box contains 2 red balls and 5 black balls . one by one , every ball is selected at random without replacement . what is the probability that the fourth ball selected is black ? \nOptions: a ) 1 / 4 , b ) 7 / 5 , c ) 1 / 2 , d ) 5 / 8 , e ) 2 / 3",
"output": [
"b"
]
},
{
"id": "task1424-222fd4f23f01426483b7cd32c048b74e",
"input": "Problem: a bag contains 6 black and 3 white balls . one ball is drawn at random . what is the probability that the ball drawn is white ? \nOptions: a ) 3 / 4 , b ) 1 / 3 , c ) 1 / 7 , d ) 1 / 8 , e ) 4 / 3",
"output": [
"b"
]
},
{
"id": "task1424-34817a9ecae0455caf542ef30caa3744",
"input": "Problem: two cards are drawn together from a pack of 52 cards the probability that one is the spade and one is a heart is ? \nOptions: a ) 85 / 852 , b ) 45 / 69 , c ) 18 / 456 , d ) 13 / 102 , e ) 23 / 125",
"output": [
"d"
]
},
{
"id": "task1424-64032d8f992a400e9b16bf4cd245a1b8",
"input": "Problem: in a lottery there are 20 prizes and 35 blanks . a lottery is drawn at random . what is the probability of getting a prize \nOptions: a ) 2 / 13 , b ) 4 / 11 , c ) 5 / 11 , d ) 6 / 11 , e ) 3 / 13",
"output": [
"b"
]
},
{
"id": "task1424-17c3a2038d8b45d9b4ec2d113d040afb",
"input": "Problem: in how many ways 4 boys and 2 girls can be seated in a row so that they are alternate . \nOptions: a ) 48 , b ) 288 , c ) 12 , d ) 256 , e ) none",
"output": [
"a"
]
},
{
"id": "task1424-276c59022f8c45fe9c5b1b615153f615",
"input": "Problem: find the probability that a leap year selected at random will not have 53 sundays or mondays . \nOptions: a ) 6 / 7 , b ) 5 / 7 , c ) 4 / 7 , d ) 3 / 7 , e ) 2 / 7",
"output": [
"c"
]
},
{
"id": "task1424-f1294d3433414ab18f9156b92a06f95a",
"input": "Problem: the probability that a number selected at random from the first 50 natural numbers is a composite number is ? \nOptions: a ) 17 / 65 , b ) 17 / 25 , c ) 17 / 28 , d ) 17 / 65 , e ) 17 / 39",
"output": [
"b"
]
},
{
"id": "task1424-e9c6fe7e658541b882f4b76afebb8923",
"input": "Problem: a certain club has 10 members , including parry . one of the 10 members is chosen at random to be the president , one of the remaining 9 members is to be chosen at random to be the secretary , and one of the remaining 8 members is to be chosen at random to be the treasurer . what is the probability that parry will be either the member chose to be secretary or the member chose to be treasurer ? \nOptions: a ) 1 / 720 , b ) 1 / 80 , c ) 1 / 10 , d ) 1 / 9 , e ) 1 / 5",
"output": [
"e"
]
},
{
"id": "task1424-726348b99bb744be8aed714832db0c39",
"input": "Problem: three 6 faced dice are thrown together . the probability that all the three show the same number on them is - \nOptions: a ) 1 / 39 , b ) 1 / 36 , c ) 1 / 32 , d ) 1 / 31 , e ) 1 / 30",
"output": [
"b"
]
},
{
"id": "task1424-452e9b4ced4549c28ef5683d8cb3bf82",
"input": "Problem: a bag contains 6 black and 8 white balls . one ball is drawn at random . what is the probability that the ball drawn is white ? \nOptions: a ) 3 / 4 , b ) 4 / 7 , c ) 1 / 7 , d ) 1 / 8 , e ) 4 / 3",
"output": [
"b"
]
},
{
"id": "task1424-68d51b0ab31d40639df5595029a525de",
"input": "Problem: a bag contains 10 red jellybeans and 10 blue jellybeans . if 3 jellybeans are removed one at a time , at random and are not replaced , what is the probability w that all 3 jellybeans removed from the bag are blue ? \nOptions: a ) 9 / 100 , b ) 2 / 19 , c ) 1 / 8 , d ) 3 / 20 , e ) 3 / 10",
"output": [
"b"
]
},
{
"id": "task1424-a0c8cfc9a8f8458290e6dd6d6011911c",
"input": "Problem: from a pack of 52 cards , two cards are drawn together at random . what is the probability of both the cards being kings ? \nOptions: a ) 1 / 15 , b ) 25 / 57 , c ) 35 / 256 , d ) 1 / 221 , e ) 2 / 15",
"output": [
"d"
]
},
{
"id": "task1424-25b0cb824663490cb0e5fc95980a80e7",
"input": "Problem: a meeting has to be conducted with 5 managers . find the number of ways in which the managers may be selected from among 9 managers , if 3 managers will not attend the meeting together . \nOptions: a ) 1.24 , b ) 2.91 , c ) 3.12 , d ) 4.126 , e ) 5.15",
"output": [
"a"
]
},
{
"id": "task1424-e3e82beac92a49d0ad4af30281b2be13",
"input": "Problem: what is the probability that a number selected from number 1 to 30 is prime number , when each of the given numbers is equally likely to be selected ? \nOptions: a ) 10 / 30 , b ) 20 / 30 , c ) 1 , d ) 5 / 30 , e ) 15 / 30",
"output": [
"a"
]
},
{
"id": "task1424-2046844ab2de49da8fe19b9253b07804",
"input": "Problem: a jar contains 6 black and 2 white balls . if you pick two balls at the same time , what ' s the probability that one ball is black and one is white ? \nOptions: a ) 2 / 7 , b ) 5 / 7 , c ) 4 / 7 , d ) 3 / 15 , e ) 3 / 14",
"output": [
"e"
]
},
{
"id": "task1424-17c09843456e4df99fa16919a1ee9639",
"input": "Problem: if two dice are thrown together , the probability of getting a doublet on the dice is \nOptions: a ) 1 / 6 , b ) 1 / 5 , c ) 1 / 4 , d ) 1 / 3 , e ) 1 / 2",
"output": [
"a"
]
},
{
"id": "task1424-326a08ed64ad48d0a21394fb41a91cdf",
"input": "Problem: a string of 25 light bulbs is wired in such a way that if any individual light bulb fails , the entire string fails . if for each individual light bulb the probability of failing during time period t is 0.06 , what is the probability that the string of light bulbs will fail during the time period t ? \nOptions: a ) 0.06 , b ) ( 0.06 ) ^ 25 , c ) 1 - ( 0.06 ) ^ 25 , d ) 1 - ( 0.94 ) ^ 25 , e ) ( 0.94 ) ^ 25",
"output": [
"d"
]
},
{
"id": "task1424-bac9a1ce7f2e4ad1bf1e51969d6e0e39",
"input": "Problem: the probability that a number selected at random from the first 50 natural numbers is a composite number is - . \nOptions: a ) 17 / 25 , b ) 17 / 27 , c ) 17 / 18 , d ) 17 / 22 , e ) 17 / 09",
"output": [
"a"
]
},
{
"id": "task1424-f26a451695ed4ed9b9568efd616930f8",
"input": "Problem: what is the probability of getting exactly 2 heads in a single throw of four fair coins ? \nOptions: a ) 1 / 2 , b ) 3 / 4 , c ) 3 / 8 , d ) 3 / 16 , e ) 5 / 16",
"output": [
"c"
]
},
{
"id": "task1424-4da97ed862eb4220b54df7c575498cb6",
"input": "Problem: in a certain animal population , for each of the first 3 months of life , the probability that an animal will die during that month is 1 / 10 . for a group of 250 newborn members of the population , approximately how many would be expected to survive the first 3 months of life ? \nOptions: a ) 140 , b ) 146 , c ) 152 , d ) 162 , e ) 183",
"output": [
"e"
]
},
{
"id": "task1424-fa63592cae584458bc918950dbee754d",
"input": "Problem: tomeka is playing a dice game . if she rolls the same number on her second roll as she rolls on her first , she wins . each roll is with two , fair , 6 - sided dice . if tomeka rolled a 7 on her first roll , what is the probability that she will win on her second roll ? \nOptions: a ) 1 / 4 , b ) 1 / 5 , c ) 1 / 6 , d ) 1 / 9 , e ) 1 / 12",
"output": [
"c"
]
},
{
"id": "task1424-a84be8fb2c9f45e98fbf9cbad5ec7a42",
"input": "Problem: two unbiased coins are tossed . what is probability of getting at most one tail ? \nOptions: a ) 12 , b ) 13 , c ) 32 , d ) 34 , e ) none of these",
"output": [
"d"
]
},
{
"id": "task1424-0958256d21c64c71babf45aef432feed",
"input": "Problem: if you throw two dice at a same time . can you find the probability of getting sum as 10 of the two numbers shown ? \nOptions: a ) 1 / 16 , b ) 2 / 14 , c ) 1 / 12 , d ) 1 / 19 , e ) 1 / 17",
"output": [
"c"
]
},
{
"id": "task1424-efff8b32b5854e638ed2f8c2031ac189",
"input": "Problem: a bag contains 3 red , 6 yellow and 8 green balls . 3 balls are drawn randomly . what is the probability that the balls drawn contain balls of different colours ? \nOptions: a ) 2 / 7 , b ) 3 / 5 , c ) 3 / 11 , d ) 18 / 85 , e ) 7 / 16",
"output": [
"d"
]
},
{
"id": "task1424-169812d1d225442aabd3db52f839f4c8",
"input": "Problem: given a bag with 2 red balls and 3 yellow balls , you randomly select one of them , in order . if the second ball you take is yellow , what is the probability that the first one was also yellow ? \nOptions: a ) 1 / 2 , b ) 1 / 5 , c ) 3 / 4 , d ) 1 / 3 , e ) 3 / 5",
"output": [
"a"
]
},
{
"id": "task1424-9f31e7c922fd47f09a60cfb65dc049a6",
"input": "Problem: in how many ways 3 boys and 3 girls can be seated in a row so that they are alternate . \nOptions: a ) 144 , b ) 288 , c ) 36 , d ) 256 , e ) none",
"output": [
"c"
]
},
{
"id": "task1424-6c09dde1bd8f4b8ea5598145f954eb37",
"input": "Problem: if x is to be chosen at random from the set { 1 , 2 , 3 , 4 } and y is to be chosen at random from the set { 5 , 6 , 7 , 8 } , what is the probability that xy will be even ? \nOptions: a ) 1 / 6 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 6",
"output": [
"c"
]
},
{
"id": "task1424-e23e73567a1548e3a4d4baf50aa36021",
"input": "Problem: when tossed , a certain coin has an equal probability of landing on either side . if the coin is tossed 4 times , what is the probability that it will land on the same side each time ? \nOptions: a ) 1 / 4 , b ) 1 / 6 , c ) 1 / 8 , d ) 1 / 12 , e ) 1 / 16",
"output": [
"c"
]
},
{
"id": "task1424-715934f9e30c4a75adb1720af0a37661",
"input": "Problem: a bag contains 2 white marbles and 2 black marbles . if each of 2 girls and 2 boys randomly selects and keeps a marble , what is the probability that all of the girls select the same colored marble ? \nOptions: a ) 1 / 35 , b ) 1 / 10 , c ) 1 / 3 , d ) 1 / 4 , e ) 1 / 5",
"output": [
"c"
]
},
{
"id": "task1424-68325a5dc5144b23856dff2da7467d01",
"input": "Problem: a bag contains 10 red jellybeans and 10 blue jellybeans . if 3 jellybeans are removed one at a time , at random and are not replaced , what is the probability t that all 3 jellybeans removed from the bag are blue ? \nOptions: a ) 9 / 100 , b ) 2 / 19 , c ) 1 / 8 , d ) 3 / 20 , e ) 3 / 10",
"output": [
"b"
]
},
{
"id": "task1424-e9f81cd71da14ff18441a03043895c47",
"input": "Problem: a meeting has to be conducted with 5 managers . find the number of ways in which the managers may be selected from among 8 managers , if 2 managers will not attend the meeting together . \nOptions: a ) 1.35 , b ) 2.91 , c ) 3.12 , d ) 4.36 , e ) 5.15",
"output": [
"d"
]
},
{
"id": "task1424-025dcaf7157c41568bbc9df1f41de0fb",
"input": "Problem: what is the probability of getting a queen or spade from a set of cards ? \nOptions: a ) 3 / 13 , b ) 4 / 13 , c ) 5 / 13 , d ) 6 / 13 , e ) 7 / 13",
"output": [
"b"
]
},
{
"id": "task1424-6d17ee1af7484b5280339b9ed6f1c04e",
"input": "Problem: if x is to be chosen at random from the set { 1 , 2 , 3 , 4 } and y is to be chosen at random from the set { 5 , 6 , 7 } , what is the probability that xy will be even ? \nOptions: a ) 1 / 6 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 6",
"output": [
"d"
]
},
{
"id": "task1424-9db982d4573940d5afc265778e814d15",
"input": "Problem: in a throw of dice what is the probability of ge æ « ng number greater than 1 \nOptions: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 5 , d ) 5 / 6 , e ) none of these",
"output": [
"e"
]
},
{
"id": "task1424-27de31a4be7548abb447ff8678ecf849",
"input": "Problem: a bag consists of 50 marbles , of which 5 are blue , 9 are red , and the remainder are white . if lisa is to select a marble from the bag at random , what is the probability that the marble will be red or white ? \nOptions: a ) 3 / 4 , b ) 2 / 4 , c ) 1 / 4 , d ) 1 / 8 , e ) 9 / 10",
"output": [
"e"
]
},
{
"id": "task1424-82562f1924924a57b07dcaf489d82b93",
"input": "Problem: a store has 10 bottles of juice , including 5 bottles of apple juice . in the evening , 6 bottles of juice are sold one by one . what is the probability of selling 3 bottles of apple juice among the 6 bottles ? assume that every bottle has an equal chance of being bought . \nOptions: a ) 4 / 9 , b ) 6 / 11 , c ) 8 / 15 , d ) 10 / 21 , e ) 12 / 25",
"output": [
"d"
]
},
{
"id": "task1424-d48051b850fe41c19eff3c41dbed7be2",
"input": "Problem: if x is to be chosen at random from the set { 1 , 2 , 3 , 4 } and y is to be chosen at random from the set { 6 , 7 } , what is the probability that xy will be even ? \nOptions: a ) 1 / 6 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 6",
"output": [
"a"
]
},
{
"id": "task1424-4f005b214a0e4dd8942b36540374a4a3",
"input": "Problem: there is a 10 % chance that tigers will not win at all during the whole season . there is a 20 % chance that federer will not play at all in the whole season . what is the greatest possible probability that the tigers will win and federer will play during the season ? \nOptions: a ) 55 % , b ) 60 % , c ) 70 % , d ) 72 % , e ) 80 %",
"output": [
"e"
]
},
{
"id": "task1424-1aec54945cb54c6cb81648f05fee480a",
"input": "Problem: a bag contains 12 red jellybeans and 12 blue jellybeans . if 3 jellybeans are removed one at a time , at random and are not replaced , what is the probability that all 3 jellybeans removed from the bag are blue ? \nOptions: a ) 9 / 100 , b ) 2 / 19 , c ) 1 / 8 , d ) 3 / 20 , e ) 3 / 10",
"output": [
"e"
]
},
{
"id": "task1424-e2b00a177e2c47ee9b443005a706481b",
"input": "Problem: in a garden , there are yellow and green flowers which are straight and curved . if the probability of picking a green flower is 1 / 8 and picking a straight flower is 1 / 2 , then what is the probability of picking a flower which is yellow and straight \nOptions: a ) 1 / 7 , b ) 1 / 8 , c ) 1 / 4 , d ) 3 / 4 , e ) 4 / 9",
"output": [
"e"
]
},
{
"id": "task1424-fd590de53113496989f2745f3b0e1c65",
"input": "Problem: a card is drawn from a pack of 52 cards the probability of getting queen of club or aking of a heart ? \nOptions: a ) 8 / 58 , b ) 9 / 25 , c ) 1 / 26 , d ) 6 / 25 , e ) 8 / 45",
"output": [
"c"
]
},
{
"id": "task1424-e2952e0e611c4c3cba6f73b19938b70f",
"input": "Problem: on a ranch , a rancher can place a loop of rope , called a lasso , once in every 3 throws around a cow ’ s neck . what is the probability that the rancher will be able to place a lasso around a cow ’ s neck at least once in 4 attempts ? \nOptions: a ) 4 / 9 , b ) 5 / 9 , c ) 17 / 27 , d ) 23 / 27 , e ) 65 / 81",
"output": [
"e"
]
},
{
"id": "task1424-3efceb7f1e80487db7622e8d726076cc",
"input": "Problem: three coins are tossed . find the probability of at most 2 tails ? \nOptions: a ) 1 / 2 , b ) 1 / 4 , c ) 2 / 3 , d ) 7 / 8 , e ) 3 / 8",
"output": [
"d"
]
},
{
"id": "task1424-a5aac41d75ee480fa119f0bd9f1029a2",
"input": "Problem: jane and thomas are among the 9 people from which a committee of 4 people is to be selected . how many different possible committees of 4 people can be selected from these 9 people if at least one of either jane or thomas is to be selected ? \nOptions: a ) 67 , b ) 73 , c ) 79 , d ) 85 , e ) 91",
"output": [
"e"
]
},
{
"id": "task1424-5160dcf8f6734554afa9d5e573ed63c5",
"input": "Problem: a fair coin is tossed 9 times . what is the probability of getting more heads than tails in 9 tosses ? \nOptions: a ) 1 / 2 , b ) 63 / 128 , c ) 4 / 7 , d ) 61 / 256 , e ) 63 / 64",
"output": [
"a"
]
},
{
"id": "task1424-8765e86329824cc09dda39fd1e9a7627",
"input": "Problem: from a group of 4 boys and 4 girls , 4 children are to be randomly selected . what is the probability that 2 boys and 2 girls will be selected ? \nOptions: a ) 12 / 29 , b ) 14 / 31 , c ) 16 / 33 , d ) 18 / 35 , e ) 20 / 37",
"output": [
"d"
]
},
{
"id": "task1424-f8d5f0eb01fa46d1ae80de8b9153e4f4",
"input": "Problem: there are 4 red shoes & 6 green shoes . if two of red shoes are drawn what is the probability of getting red shoes \nOptions: a ) 1 / 13 , b ) 1 / 14 , c ) 1 / 2 , d ) 2 / 15 , e ) 2 / 16",
"output": [
"d"
]
},
{
"id": "task1424-be099bbb98544fb7b48d5ddc35018d12",
"input": "Problem: in how many ways can 21 books on english and 19 books on hindi be placed in a row on a shelf so that two books on hindi may not be together ? \nOptions: a ) 1540 , b ) 2314 , c ) 5420 , d ) 1240 , e ) 4512",
"output": [
"a"
]
},
{
"id": "task1424-f1ca597d2d9e4cd88ad9331985ebd456",
"input": "Problem: from a pack of 52 cards , 1 card is drawn at random . what is the probability that a heart is drawn ? \nOptions: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 13 , e ) 3 / 26",
"output": [
"c"
]
},
{
"id": "task1424-8f6ce3adbea34b62a3ec581df89a95d6",
"input": "Problem: there are 4 books on a shelf , of which 3 are paperbacks and 6 are hardbacks . how many possible selections of 4 books from this shelf include at least one paperback ? \nOptions: a ) a ) 40 , b ) b ) 45 , c ) c ) 50 , d ) d ) 55 , e ) e ) 111",
"output": [
"e"
]
},
{
"id": "task1424-150d07043c4c451da9256e0a8327f81e",
"input": "Problem: on a ranch , a rancher can place a loop of rope , called a lasso , once in every 3 throws around a cow ’ s neck . what is the probability that the rancher will be able to place a lasso around a cow ’ s neck at least once in 3 attempts ? \nOptions: a ) 1 / 3 , b ) 5 / 9 , c ) 7 / 9 , d ) 19 / 27 , e ) 23 / 27",
"output": [
"d"
]
},
{
"id": "task1424-b7c6dd33f0c5429796283282fc929e82",
"input": "Problem: there are 8 pairs of socks and 2 socks are worn from that such that the pair of socks worn are not of the same pair . what is the number of pair that can be formed . \nOptions: a ) 53 , b ) 54 , c ) 55 , d ) 56 , e ) 57",
"output": [
"d"
]
},
{
"id": "task1424-cadf3226dd074cbca147e3a765034a46",
"input": "Problem: how many positive integers less than 400 can be formed using the numbers 1 , 2 , 3 and 5 for the digits ? \nOptions: a ) 48 , b ) 52 , c ) 66 , d ) 84 , e ) 68",
"output": [
"e"
]
},
{
"id": "task1424-4a94fa1d276d4676ad60ddbf080fad9d",
"input": "Problem: if x is to be chosen at random from the set { 1 , 2 , 3 } and y is to be chosen at random from the set { 5 , 6 , 7 } , what is the probability that xy will be even ? \nOptions: a ) 1 / 6 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 6",
"output": [
"e"
]
},
{
"id": "task1424-1678c2d46abe448a83280e28fe22a72f",
"input": "Problem: in a lottery there are 100 prizes and 300 blanks . a lottery is drawn at random . what is the probability of getting a prize ? \nOptions: a ) 1 / 2 , b ) 5 / 400 , c ) 1 / 5 , d ) 1 / 3 , e ) 1 / 4",
"output": [
"e"
]
},
{
"id": "task1424-03c65135c7b548db943cc4df67438020",
"input": "Problem: if a coin is flipped , the probability that the coin will land heads is 1 / 2 . if the coin is flipped 5 times , what is the probability that it will land tails up on the first 4 flips and not on the last flip ? \nOptions: a ) 1 / 8 , b ) 1 / 32 , c ) 1 / 4 , d ) 1 / 2 , e ) 1 / 16",
"output": [
"b"
]
},
{
"id": "task1424-a730119273af4670a3110d8ea487160f",
"input": "Problem: three unbiased coins are tossed . what is the probability of getting 3 heads ? \nOptions: a ) 3 / 4 , b ) 1 / 4 , c ) 3 / 8 , d ) 7 / 8 , e ) 1 / 8",
"output": [
"e"
]
},
{
"id": "task1424-275565d7339a42bd92a87f4182e43a63",
"input": "Problem: a bag contains 10 red jellybeans and 10 blue jellybeans . if 3 jellybeans are removed one at a time , at random and are not replaced , what is the probability q that all 3 jellybeans removed from the bag are blue ? \nOptions: a ) 9 / 100 , b ) 2 / 19 , c ) 1 / 8 , d ) 3 / 20 , e ) 3 / 10",
"output": [
"b"
]
},
{
"id": "task1424-846f989ba72642d9be486ab9628bb0a9",
"input": "Problem: how many different ways can 2 students be seated in a row of 8 desks , so that there is always at least one empty desk between the students ? \nOptions: a ) 50 , b ) 42 , c ) 24 , d ) 20 , e ) 12",
"output": [
"b"
]
},
{
"id": "task1424-33fc4788620d4a2188308222b2f41edc",
"input": "Problem: if a card is drawn from a well shuffled pack of cards , the probability of drawing a spade or a king is - \nOptions: a ) 8 / 13 , b ) 6 / 13 , c ) 3 / 13 , d ) 4 / 13 , e ) 1 / 13",
"output": [
"d"
]
},
{
"id": "task1424-25c6cfcd901c4786a56d04d979c3b21e",
"input": "Problem: there are 7 books on a shelf , of which 2 are paperbacks and 5 are hardbacks . how many possible selections of 4 books from this shelf include at least one paperback ? \nOptions: a ) a ) 30 , b ) b ) 45 , c ) c ) 50 , d ) d ) 55 , e ) e ) 60",
"output": [
"a"
]
},
{
"id": "task1424-2d2a229a38a54a9aa55968b3125a45d3",
"input": "Problem: in 15 year ’ s time the combined age of my 4 brothers will be 107 . what will it be in 6 year ’ s time ? \nOptions: a ) 65 , b ) 87 , c ) 71 , d ) 60 , e ) 66",
"output": [
"c"
]
},
{
"id": "task1424-10d298d55bb34698bfb36d6bc329ed41",
"input": "Problem: a box contains 20 electric bulbs , out of which 4 are defective . two bulbs are chosen at random from this box . the probability that at least one of these is defective is \nOptions: a ) 7 / 19 , b ) 6 / 19 , c ) 5 / 19 , d ) 4 / 19 , e ) none of these",
"output": [
"a"
]
},
{
"id": "task1424-374441187626495ca2d2fd763cfb7f09",
"input": "Problem: find the probability that a leap year selected at random will not have 53 sundays \nOptions: a ) 6 / 7 , b ) 5 / 7 , c ) 4 / 7 , d ) 3 / 7 , e ) 2 / 7",
"output": [
"b"
]
},
{
"id": "task1424-bcf1bcf57eb24a6c9ddd88b5be2b14d3",
"input": "Problem: if two dice are thrown together , the probability of getting an even number on one die and an odd number on the other is ? \nOptions: a ) 1 / 9 , b ) 1 / 2 , c ) 1 / 1 , d ) 1 / 5 , e ) 1 / 8",
"output": [
"b"
]
},
{
"id": "task1424-0383163efeab4ce890d74f5d32b7fe6a",
"input": "Problem: a bag contains 6 black and 5 white balls . one ball is drawn at random . what is the probability that the ball drawn is white ? \nOptions: a ) 3 / 4 , b ) 5 / 11 , c ) 1 / 7 , d ) 1 / 8 , e ) 4 / 3",
"output": [
"b"
]
},
{
"id": "task1424-0b39db3ad7b64285989dcb0002ad3da0",
"input": "Problem: three 6 faced dice are thrown together . the probability that exactly two dice show the same number on them is \nOptions: a ) 5 / 15 , b ) 5 / 12 , c ) 5 / 19 , d ) 5 / 12 , e ) 5 / 11",
"output": [
"b"
]
},
{
"id": "task1424-b0133d86302a401088ee96774b8a0c7e",
"input": "Problem: rhoda tosses a coin 5 times . find the probability of getting exactly 4 heads . \nOptions: a ) 5 / 32 , b ) 6 / 32 , c ) 5 / 16 , d ) 4 / 32 , e ) 8 / 32",
"output": [
"a"
]
},
{
"id": "task1424-57314c989e454b82ae61dfa2c3ed28d8",
"input": "Problem: from a pack of cards , two cards are drawn one after the other , with replacement . what is the probability that the first card is a club and the second card is a king or queen ? \nOptions: a ) 2 / 13 , b ) 3 / 13 , c ) 1 / 26 , d ) 1 / 52 , e ) 3 / 52",
"output": [
"c"
]
},
{
"id": "task1424-8dea9c93201641faac499dd3634f84f0",
"input": "Problem: a box contains 3 red balls and 4 black balls . one by one , every ball is selected at random without replacement . what is the probability that the fourth ball selected is black ? \nOptions: a ) 7 / 4 , b ) 1 / 2 , c ) 1 / 2 , d ) 5 / 8 , e ) 2 / 3",
"output": [
"a"
]
},
{
"id": "task1424-b01693fa4fed4ce88e9176bb2d88be6f",
"input": "Problem: the probability that a number selected at random from first 50 natural numbers is a composite number is \nOptions: a ) 21 / 25 , b ) 17 / 25 , c ) 4 / 25 , d ) 8 / 25 , e ) 10 / 25",
"output": [
"b"
]
},
{
"id": "task1424-f8143a9a3d4a469ab799051865c2950f",
"input": "Problem: in a throw of dice what is the probability of getting number greater than 5 \nOptions: a ) 1 / 7 , b ) 1 / 6 , c ) 1 / 11 , d ) 1 / 13 , e ) 2 / 9",
"output": [
"b"
]
},
{
"id": "task1424-c7ab9020f2ae40f98ba48dad930f31e3",
"input": "Problem: if a certain coin is flipped , the probability that the coin will land heads is 1 / 2 . if the coin is flipped 6 times , what is the probability that it will land heads up on the first 3 flips but not on the last 3 flips ? \nOptions: a ) 1 / 8 , b ) 1 / 16 , c ) 1 / 32 , d ) 1 / 64 , e ) 1 / 128",
"output": [
"d"
]
},
{
"id": "task1424-259f4ccd2b354fa3adf4588efa97dfa2",
"input": "Problem: from a group of 3 boys and 3 girls , 4 children are to be randomly selected . what is the probability that equal numbers of boys and girls will be selected ? \nOptions: a ) 1 / 10 , b ) 4 / 9 , c ) 1 / 2 , d ) 3 / 5 , e ) 2 / 3",
"output": [
"d"
]
},
{
"id": "task1424-6ac58a9c34f241ee9b91b8ad59fe0ba5",
"input": "Problem: in a bag containing 3 balls , a white ball was placed and then 1 ball was taken out at random . what isthe probability that theextracted ball would turn on to be white , if all possible hypothesis concerning the color of the balls that initially in the bag were equally possible ? \nOptions: a ) 2 / 3 , b ) 5 / 8 , c ) 3 / 5 , d ) 4 / 7 , e ) 5 / 8",
"output": [
"b"
]
},
{
"id": "task1424-3b1fcf8b8a4f4d9d95c4ccce282bf1fa",
"input": "Problem: wink , inc . follows a certain procedure that requires two tasks to be finished independently in order for a job to be done . on any given day , there is a 2 / 3 probability that task 1 will be completed on time , and a 3 / 5 probability that task 2 will be completed on time . on a certain day , what is the probability that task 1 will be completed on time , but task 2 will not ? \nOptions: a ) 4 / 15 , b ) 3 / 40 , c ) 13 / 40 , d ) 7 / 20 , e ) 13 / 22",
"output": [
"a"
]
},
{
"id": "task1424-6cac330f0ad1463fb653e104d335ac29",
"input": "Problem: a certain junior class has 1000 students and a certain senior class has 800 students . among these students , there are 60 siblings pairs each consisting of 1 junior and 1 senior . if 1 student is to be selected at random from each class , what is the probability that the 2 students selected will be a sibling pair ? \nOptions: a ) 3 / 40000 , b ) 1 / 3600 , c ) 9 / 2000 , d ) 1 / 60 , e ) 1 / 15",
"output": [
"a"
]
},
{
"id": "task1424-e50fb9912278426fbddb7f7956c46e88",
"input": "Problem: in how many ways 2 boys and 2 girls can be seated in a row so that boys and girls are alternate ? \nOptions: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11",
"output": [
"b"
]
},
{
"id": "task1424-5218b0d6353249aaadb61b6c58307874",
"input": "Problem: two mba admissions committees are to be formed randomly from 6 second year mbas with 3 members each . what is the probability that jane will be on the same committee as albert ? \nOptions: a ) 12 % , b ) 20 % , c ) 33 % , d ) 40 % , e ) 50 %",
"output": [
"d"
]
},
{
"id": "task1424-4f9c4437ac744b1eb3c5c39f31bfd91d",
"input": "Problem: a bag contains 3 white marbles and 3 black marbles . if each of 3 girls and 3 boys randomly selects and keeps a marble , what is the probability that all of the girls select the same colored marble ? \nOptions: a ) 1 / 35 , b ) 1 / 10 , c ) 1 / 15 , d ) 1 / 20 , e ) 1 / 25",
"output": [
"b"
]
},
{
"id": "task1424-31707f803d1a4a51ac2391ee36c81c4a",
"input": "Problem: when tossed , a certain coin has equal probability of landing on either side . if the coin is tossed 3 times , what is the probability that it will land on the same side each time ? \nOptions: a ) 1 / 8 , b ) 1 / 4 , c ) 1 / 3 , d ) 3 / 8 , e ) 1 / 2",
"output": [
"b"
]
},
{
"id": "task1424-6902a759bd074bd89001e33ceab3a718",
"input": "Problem: a basket contains 7 apples , of which 1 is spoiled and the rest are good . if we select 2 apples from the basket simultaneously and at random , what is the probability that the 2 apples selected will include the spoiled apple ? \nOptions: a ) 1 / 5 , b ) 2 / 7 , c ) 2 / 9 , d ) 3 / 5 , e ) 4 / 11",
"output": [
"b"
]
},
{
"id": "task1424-6914019ffb4d4992921cf4b3e57a1ddd",
"input": "Problem: from a pack of 52 cards , 1 card is drawn at random . what is the probability that a red king is drawn ? \nOptions: a ) 1 / 2 , b ) 1 / 4 , c ) 1 / 13 , d ) 1 / 26 , e ) 1 / 52",
"output": [
"d"
]
},
{
"id": "task1424-f54544120e5e48f4ab815f69ebe15766",
"input": "Problem: 45 girls and 60 boys are present at a party . there are 17 girl - boy are in relationship among them . if a girl and a boy is selected at random , what is the probability that they will be a couple ? \nOptions: a ) 1 / 200 , b ) 1 / 100 , c ) 90 / 2900 , d ) 17 / 2700 , e ) 1 / 20",
"output": [
"d"
]
},
{
"id": "task1424-2a70208cb737482bb2a1e145035a2579",
"input": "Problem: if a coin is flipped , the probability that the coin will land tails is 1 / 2 . if the coin is flipped 4 times , what is the probability that it will land tails up on the first 2 flips and not on the last 2 flips ? \nOptions: a ) 1 / 4 , b ) 1 / 8 , c ) 1 / 2 , d ) 1 / 16 , e ) 1 / 32",
"output": [
"d"
]
},
{
"id": "task1424-61b44f626b064719bfc41aea11ba5fbf",
"input": "Problem: a bag contains 10 black and 20 white balls . one ball is drawn at random . what is the probability that the ball drawn is white ? \nOptions: a ) 1 / 2 , b ) 3 / 4 , c ) 2 / 3 , d ) 1 / 5 , e ) 3 / 7",
"output": [
"c"
]
},
{
"id": "task1424-df240844c977487d82c64f2ff8ebdb2a",
"input": "Problem: a bag contains 6 red , 2 yellow and 4 green balls . 3 balls are drawn randomly . what is the probability that the balls drawn contain balls of different colours ? \nOptions: a ) 12 / 55 , b ) 3 / 5 , c ) 3 / 11 , d ) 1 / 4 , e ) 7 / 16",
"output": [
"a"
]
},
{
"id": "task1424-abd9b8b804464bca8b2d67accd6b72ee",
"input": "Problem: a question paper has 2 parts , a & b , each containing 8 questions . if a student has to choose 8 from part a & 4 from part b , in how many ways can he choose the questions ? \nOptions: a ) 110 , b ) 70 , c ) 120 , d ) 130 , e ) 140",
"output": [
"b"
]
},
{
"id": "task1424-f33beff80ec34042b3edc61bdcde6a8b",
"input": "Problem: a jar contains 18 balls . 3 blue balls are removed from the jar and not replaced . now the probability of getting a blue ball is 1 / 5 then how many blue balls jar contains initially ? \nOptions: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6",
"output": [
"e"
]
},
{
"id": "task1424-4756551235964f70a347095c7366365c",
"input": "Problem: there are 6 red balls and 4 blue balls in a jar . if 3 balls are selected from the jar , what is the probability that all 3 balls selected are blue balls ? \nOptions: a ) 1 / 18 , b ) 1 / 24 , c ) 1 / 30 , d ) 1 / 36 , e ) 1 / 48",
"output": [
"c"
]
},
{
"id": "task1424-c59a2819c3274f4a908b2df3002726cd",
"input": "Problem: when you draw 2 dices together , find the probability of getting a total of 6 ? \nOptions: a ) 3 / 13 , b ) 2 / 31 , c ) 5 / 36 , d ) 7 / 41 , e ) 7 / 43",
"output": [
"c"
]
},
{
"id": "task1424-31520dd804934a46940bf3880ee22c8c",
"input": "Problem: there are 20 balls in a jar . you take out 2 blue balls without putting them back inside , and now the probability of pulling out a blue ball is 1 / 5 . how many blue balls were there in the beginning ? \nOptions: a ) 12 . , b ) 9 . , c ) 8 . , d ) 7 . , e ) 6 .",
"output": [
"a"
]
},
{
"id": "task1424-69096a1cafba4cfb940981926878b72c",
"input": "Problem: a bag contains 3 red , 5 yellow and 7 green balls . 3 balls are drawn randomly . what is the probability that the balls drawn contain balls of different colours ? \nOptions: a ) 2 / 7 , b ) 3 / 5 , c ) 3 / 13 , d ) 1 / 4 , e ) 7 / 16",
"output": [
"c"
]
},
{
"id": "task1424-34231ee3885944d8bc1e64440fd3f19c",
"input": "Problem: 4 dice are thrown simultaneously on the board . find the probability show the same face . \nOptions: a ) 1 / 213 , b ) 1 / 215 , c ) 1 / 216 , d ) 2 / 113 , e ) 3 / 114",
"output": [
"c"
]
},
{
"id": "task1424-3e41afb759904e69b15b229d74e0b7fd",
"input": "Problem: what is the probability that a two digit number selected at random is a multiple of 3 and not a multiple of 5 ? \nOptions: a ) 1 / 15 , b ) 2 / 15 , c ) 4 / 15 , d ) 7 / 15 , e ) none of these",
"output": [
"c"
]
},
{
"id": "task1424-298301e639ff473894cd81c92bc05caa",
"input": "Problem: in a throw of a coin probability of getting a head . \nOptions: a ) 1 / 3 , b ) 2 / 3 , c ) 1 / 4 , d ) 2 / 5 , e ) 1 / 2",
"output": [
"e"
]
},
{
"id": "task1424-b8159b8b262c45488485ac38dcdca030",
"input": "Problem: a box contains 100 balls , numbered from 1 to 100 . if 3 balls are selected at random and with replacement from the box . if the 3 numbers on the balls selected contain two odd and one even . what is the probability j that the first ball picked up is odd numbered ? \nOptions: a ) 0 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 1",
"output": [
"d"
]
},
{
"id": "task1424-1ade2bba793c458899ae6691cb3692fb",
"input": "Problem: it takes 60 identical printing machines 4 hours to print 200,000 cards . how long would it take 50 of these machines to print the same total ? \nOptions: a ) 10 hr , b ) 5 hr , c ) 6 hr , d ) 4 hr 30 min , e ) 5 hr 12 min",
"output": [
"e"
]
},
{
"id": "task1424-cd43f5562cb146b9a2768b5dc2e3a71a",
"input": "Problem: if 4 people are selected from a group of 10 married couples , what is the probability that none of them would be married to each other ? \nOptions: a ) 1 / 33 , b ) 2 / 63 , c ) 1 / 3 , d ) 43 / 62 , e ) 11 / 12",
"output": [
"d"
]
},
{
"id": "task1424-5a1a0c8821fb42f7954a51ceaaac358b",
"input": "Problem: john borrowed 3 soccer boots from jake , and forgot them on the field , if peter came across a total of 15 boots on the field jake ' s boots inclusive , and he took 4 boots at random , what is the probability that jake ' s boots were not amongst the 4 taken ? . \nOptions: a ) 12 / 91 , b ) 3 / 15 , c ) 12 / 15 , d ) 33 / 91 , e ) 3 / 91",
"output": [
"d"
]
},
{
"id": "task1424-b6d8ce14f4d24364b57d31442c850286",
"input": "Problem: kim has 8 pairs of shoes ; each pair is a different color . if kim randomly selects 2 shoes without replacement from the 16 shoes , what is the probability that she will select 2 shoes of the same color ? \nOptions: a ) 2 / 5 , b ) 1 / 5 , c ) 1 / 9 , d ) 1 / 10 , e ) 1 / 15",
"output": [
"e"
]
},
{
"id": "task1424-f0f5ec6676f34897b33ad719481325a4",
"input": "Problem: two coins are tossed . find the probability of at most 2 tails ? \nOptions: a ) 1 / 2 , b ) 1 / 4 , c ) 1 / 3 , d ) 1 , e ) 3 / 4",
"output": [
"d"
]
},
{
"id": "task1424-d9dd7abb89644b89bd281fef535cfd25",
"input": "Problem: an urn contains 5 red , 6 blue and 8 green balls . 4 balls are randomly selected from the urn , find the probability that the drawn ball are 1 blue and 2 red and 1 green balls ? \nOptions: a ) 20 / 323 , b ) 40 / 323 , c ) 60 / 273 , d ) 50 / 373 , e ) 40 / 373",
"output": [
"b"
]
},
{
"id": "task1424-d74b2beb662b498583b4df27f4978908",
"input": "Problem: x , y , and z are all unique numbers . if x is chosen randomly from the set { 6 , 7 , 8 , 9 , 10 , 11 } and y and z are chosen randomly from the set { 20 , 21 , 22 , 23 } , what is the probability that x and y are prime and z is not ? \nOptions: a ) 1 / 5 , b ) 3 / 20 , c ) 2 / 15 , d ) 1 / 12 , e ) 1 / 10",
"output": [
"d"
]
},
{
"id": "task1424-c92fb4f23fdc41cc9222127f445796c4",
"input": "Problem: when tossed , a certain coin has an equal probability of landing on either side . if the coin is tossed 5 times , what is the probability that it will land on the same side each time ? \nOptions: a ) 1 / 6 , b ) 1 / 8 , c ) 1 / 12 , d ) 1 / 16 , e ) 1 / 32",
"output": [
"d"
]
},
{
"id": "task1424-0539910c006d4bf092de19031da5ec6c",
"input": "Problem: from a pack of cards , two cards are drawn one after the other , with replacement . what is the probability that the first card is a club and the second card is a red king ? \nOptions: a ) 1 / 13 , b ) 1 / 15 , c ) 1 / 26 , d ) 1 / 52 , e ) 1 / 104",
"output": [
"e"
]
},
{
"id": "task1424-653dc611eb2e4976a6678d716f7a4994",
"input": "Problem: what is the probability that the sum of two dice will yield a 6 , and then when both are thrown again , their sum will again yield a 6 ? assume that each die has 5 sides with faces numbered 1 to 5 . \nOptions: a ) 1 / 144 , b ) 1 / 25 , c ) 1 / 12 , d ) 1 / 6 , e ) 1 / 3",
"output": [
"b"
]
},
{
"id": "task1424-8a57af7cf6cd47218106831518501a99",
"input": "Problem: from a pack of 52 cards , 1 card is drawn at random . find the probability of a face card drawn . \nOptions: a ) 4 / 13 , b ) 1 / 52 , c ) 1 / 4 , d ) 1 / 3 , e ) none of these",
"output": [
"a"
]
},
{
"id": "task1424-2e8c90fa84b343bc99d2d241aa6d5ae4",
"input": "Problem: in a certain animal population , for each of the first 3 months of life , the probability that an animal will die during that month is 1 / 8 . for a group of 200 newborn members of the population , approximately how many would be expected to survive the first 3 months of life ? \nOptions: a ) 134 , b ) 146 , c ) 152 , d ) 162 , e ) 170",
"output": [
"a"
]
},
{
"id": "task1424-ed6ae6c7374e49b7801a01fbdc6004cd",
"input": "Problem: at a conference table , 6 employees gather around a table . one of the employees is the manager and he sits at the head of the table . two of the employees sit on either side of the table . how many different seating arrangements can be made with these 6 employees ? \nOptions: a ) 60 , b ) 80 , c ) 100 , d ) 120 , e ) 140",
"output": [
"d"
]
},
{
"id": "task1424-c36b0145df3948bd9e249ee7f2dc3dbf",
"input": "Problem: a jar contains only red , yellow , and orange marbles . if there are 3 red , 3 yellow , and 4 orange marbles , and 3 marbles are chosen from the jar at random without replacing any of them , what is the probability that 2 yellow , 1 red , and no orange marbles will be chosen ? \nOptions: a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 5 / 22",
"output": [
"c"
]
},
{
"id": "task1424-322b51ce99ba4e3fb6ef57c87fb3a9a5",
"input": "Problem: wink , inc . follows a certain procedure that requires two tasks to be finished independently in order for a job to be done . on any given day , there is a 1 / 8 probability that task 1 will be completed on time , and a 3 / 5 probability that task 2 will be completed on time . on a certain day , what is the probability that task 1 will be completed on time , but task 2 will not ? \nOptions: a ) 1 / 20 , b ) 3 / 40 , c ) 13 / 40 , d ) 7 / 20 , e ) 13 / 22",
"output": [
"a"
]
},
{
"id": "task1424-f7aa13c3ea9043a894ab648ea6d3e5c0",
"input": "Problem: there are 10 books on a shelf , of which 4 are paperbacks and 6 are hardbacks . how many possible selections of 5 books from the shelf contain at least one paperback and at least one hardback ? \nOptions: a ) 75 , b ) 120 , c ) 210 , d ) 246 , e ) 252",
"output": [
"d"
]
},
{
"id": "task1424-988ccb7221f944f2b2941ad934c4f7ac",
"input": "Problem: a bag contains 3 red , 2 yellow and 4 green balls . 3 balls are drawn randomly . what is the probability that the balls drawn contain balls of different colours ? \nOptions: a ) 2 / 7 , b ) 3 / 5 , c ) 3 / 11 , d ) 1 / 4 , e ) 7 / 16",
"output": [
"a"
]
},
{
"id": "task1424-de6fff91bffb4f17abd2736a2539f1f7",
"input": "Problem: find the probability that the number drawn is a multiple of 6 and 8 . \nOptions: a ) 3 / 50 , b ) 2 / 25 , c ) 1 / 50 , d ) 1 / 25 , e ) 4 / 25",
"output": [
"d"
]
},
{
"id": "task1424-dbbcaf06e8364706b68f12b3bd9461fd",
"input": "Problem: jane and thomas are among the 7 people from which a committee of 4 people is to be selected . how many different possible committees of 4 people can be selected from these 7 people if at least one of either jane or thomas is to be selected ? \nOptions: a ) 30 , b ) 45 , c ) 55 , d ) 65 , e ) 70",
"output": [
"a"
]
},
{
"id": "task1424-e5621bccd99c4190b468972079944a2e",
"input": "Problem: there are 8 books on a shelf , of which 2 are paperbacks and 6 are hardbacks . how many possible selections of 3 books from this shelf include at least one paperback ? \nOptions: a ) a ) 40 , b ) b ) 45 , c ) c ) 36 , d ) d ) 55 , e ) e ) 60",
"output": [
"c"
]
},
{
"id": "task1424-0c5fe1636e664985af13f88a97a90407",
"input": "Problem: in a bag containing 5 balls , a white ball was placed and then 1 ball was taken out at random . what is the probability that the extracted ball would turn on to be white , if all possible hypothesis concerning the color of the balls that initiallyin the bag wereequally possible ? \nOptions: a ) 2 / 3 , b ) 5 / 8 , c ) 5 / 4 , d ) 5 / 6 , e ) 6 / 7",
"output": [
"b"
]
},
{
"id": "task1424-2032feac0bba4db18b3db549e8121243",
"input": "Problem: a bag contains 3 blue and 5 white marbles . one by one , marbles are drawn out randomly until only two are left in the bag . what is the probability w that out of the two , one is white and one is blue ? \nOptions: a ) 15 / 56 , b ) 41 / 56 , c ) 13 / 28 , d ) 15 / 28 , e ) 5 / 14",
"output": [
"d"
]
},
{
"id": "task1424-13682b690bfb40d092f532b2f849ad4d",
"input": "Problem: what is the probability of getting 53 mondays in a leap year ? \nOptions: a ) 1 / 7 , b ) 2 / 7 , c ) 3 / 7 , d ) 4 / 7 , e ) 5 / 7",
"output": [
"b"
]
},
{
"id": "task1424-04213bdf3cc04da7a7dffe63cc66bd36",
"input": "Problem: what is the probability that company g ' s advertisement will be one of the first two be shown during the first commercial break ? \nOptions: a ) 1 / 225 , b ) 1 / 30 , c ) 1 / 15 , d ) 2 / 15 , e ) 4 / 15",
"output": [
"d"
]
},
{
"id": "task1424-c87eeeb847994b5c9c14ea7fb6cc599f",
"input": "Problem: a father purchased dress for his 3 daughters . the dresses are of same color but diff size and they are kept in dark room . what is probability that all the 3 will not choose their own dress ? \nOptions: a ) 22 , b ) 87 , c ) 29 , d ) 26 , e ) 191",
"output": [
"b"
]
},
{
"id": "task1424-615e92b9aa9249619308283a3c22136e",
"input": "Problem: a meeting has to be conducted with 6 managers . find the number of ways in which the managers be selected from among 10 managers , if 2 managers will not attend the meeting together ? \nOptions: a ) 120 , b ) 110 , c ) 105 , d ) 140 , e ) 135",
"output": [
"d"
]
},
{
"id": "task1424-70a51d4148614a7aa9b11e5ff9f08a1b",
"input": "Problem: a store has 10 bottles of juice , including 6 bottles of apple juice . in the evening , 6 bottles of juice are sold one by one . what is the probability of selling 3 bottles of apple juice among the 6 bottles ? assume that every bottle has an equal chance of being bought . \nOptions: a ) 2 / 11 , b ) 4 / 15 , c ) 6 / 17 , d ) 8 / 21 , e ) 10 / 25",
"output": [
"d"
]
},
{
"id": "task1424-a40cc64c517b41ea9af654fb5d90e63f",
"input": "Problem: x , y , and z are all unique numbers . if x is chosen randomly from the set { 10 , 11 } and y and z are chosen randomly from the set { 20 , 21 , 22 , 23 } , what is the probability that x and y are prime and z is not ? \nOptions: a ) 1 / 5 , b ) 3 / 20 , c ) 1 / 8 , d ) 3 / 10 , e ) 1 / 10",
"output": [
"c"
]
},
{
"id": "task1424-dc67d45babca4d4ca138d6c062c63757",
"input": "Problem: a coin is tossed 8 times . what is the probability of getting exactly 7 heads ? \nOptions: a ) 1 / 8 , b ) 1 / 16 , c ) 1 / 32 , d ) 1 / 64 , e ) 1 / 128",
"output": [
"c"
]
},
{
"id": "task1424-2ade14b434fd40b193ee8157714f9c16",
"input": "Problem: how many positive integers less than 500 can be formed using the numbers 1 , 2 , 3 and 5 for the digits ? \nOptions: a ) 48 , b ) 52 , c ) 66 , d ) 68 , e ) 84",
"output": [
"d"
]
},
{
"id": "task1424-bffa6ca7a7b64538b59481db40ba356d",
"input": "Problem: there are 6 different travelers who each have a choice of vacationing at one of 10 different destinations . what is the probability that all 6 travelers will end up vacationing at the same destination ? \nOptions: a ) 0.1 , b ) 0.001 , c ) 0.0002 , d ) 1.0 e - 05 , e ) 0.0001",
"output": [
"d"
]
},
{
"id": "task1424-47b4af2d92af4f188d262f76f110bd86",
"input": "Problem: if two dice are thrown together , the probability of getting an even number on one die and an odd number on the other is - . \nOptions: a ) 1 / 3 , b ) 1 / 2 , c ) 7 / 8 , d ) 3 / 4 , e ) 7 / 3",
"output": [
"b"
]
},
{
"id": "task1424-3abb52f9c50d49d9a004de5ed454e669",
"input": "Problem: a certain junior class has 1,200 students and a certain senior class has 800 students . among these students , there are 60 siblings pairs , each consisting of 1 junior and 1 senior . if 1 student is to be selected at random from each class , what is the probability that the 2 students selected at will be a sibling pair ? \nOptions: a ) 3 / 40,000 , b ) 1 / 3,600 , c ) 9 / 2,000 , d ) 1 / 60 , e ) 1 / 16,000",
"output": [
"e"
]
},
{
"id": "task1424-a47765ee878e4b0f87f0a87a72f68eb4",
"input": "Problem: a box contains 22 electric bulbs , out of which 4 are defective . two bulbs are chosen at random from this box . the probability that at least one of these is defective is \nOptions: a ) 4 / 19 , b ) 7 / 19 , c ) 12 / 19 , d ) 21 / 99 , e ) 26 / 77",
"output": [
"e"
]
},
{
"id": "task1424-0c1690f488164189af88157859ac2b74",
"input": "Problem: a fair coin is tossed 3 times . what is the probability of getting at least 2 heads ? \nOptions: a ) 3 / 4 , b ) 3 / 2 , c ) 1 / 4 , d ) 1 / 2 , e ) 1 / 5",
"output": [
"d"
]
},
{
"id": "task1424-98d1a053534c4f7dab13573f5fb6b9b3",
"input": "Problem: a coin is tossed 3 times . what is the probability of getting exactly 2 heads ? \nOptions: a ) 1 / 2 , b ) 1 / 4 , c ) 3 / 8 , d ) 5 / 8 , e ) 3 / 16",
"output": [
"c"
]
},
{
"id": "task1424-6e49ad2f93ca4e86a4fc4b7cd8a4a059",
"input": "Problem: an urn contains 5 red , 6 blue and 8 green balls . 4 balls are randomly selected from the urn , find the probability that the drawn ball are 1 blue and 1 red and 2 green balls ? \nOptions: a ) 70 / 323 , b ) 50 / 323 , c ) 52 / 969 , d ) 60 / 323 , e ) 25 / 321",
"output": [
"a"
]
},
{
"id": "task1424-91815ac4d7d74c41bc07716bcc5164a3",
"input": "Problem: how many cubes of 3 cm edge can be cut out of a cube of 18 cm edge \nOptions: a ) 36 , b ) 232 , c ) 216 , d ) 455 , e ) 363",
"output": [
"c"
]
},
{
"id": "task1424-3840d6e599f64bb6a7ad4b28388a1569",
"input": "Problem: two mba admissions committees are to be formed randomly from 6 second year mbas with 3 members each . what is the probability v that jane will be on the same committee as albert ? \nOptions: a ) 12 % , b ) 20 % , c ) 33 % , d ) 40 % , e ) 50 %",
"output": [
"d"
]
},
{
"id": "task1424-059fe8a309854e05a77a7f725b65577c",
"input": "Problem: on a ranch , a rancher can place a loop of rope , called a lasso , once in every 2 throws around a cow ’ s neck . what is the probability that the rancher will be able to place a lasso around a cow ’ s neck at least once in 6 attempts ? \nOptions: a ) 3 / 4 , b ) 7 / 8 , c ) 15 / 16 , d ) 31 / 32 , e ) 63 / 64",
"output": [
"e"
]
},
{
"id": "task1424-7b0828536449414ca206208b3f3cff40",
"input": "Problem: what is the probability of getting a sum 9 from two throws of dice . \nOptions: a ) 1 / 3 , b ) 1 / 9 , c ) 1 / 12 , d ) 2 / 9 , e ) none of these",
"output": [
"b"
]
},
{
"id": "task1424-b672738b1ba348889db8bca1ed73254a",
"input": "Problem: if a card is drawn from a well shuffled deck of cards , what is the probability of drawing a black card or a face card ? \nOptions: a ) 7 / 13 , b ) 15 / 26 , c ) 9 / 12 , d ) 8 / 13 , e ) 29 / 52",
"output": [
"d"
]
},
{
"id": "task1424-68917b28ff6143ccb752fae5fdf8a7fb",
"input": "Problem: how many cubes of 2 cm edge can be cut out of a cube of 24 cm edge \nOptions: a ) 1136 , b ) 1728 , c ) 1216 , d ) 1484 , e ) none of these",
"output": [
"b"
]
},
{
"id": "task1424-f2607de75413499d9ebcd71c84ed8dcb",
"input": "Problem: the chance of rain on any given day in tel - aviv is 50 % . what is the probability z that it rained in tel - aviv on exactly 4 out of 6 randomly chosen days ? \nOptions: a ) 15 / 64 , b ) 30 / 64 , c ) 1 / 2 , d ) 1 / 4 , e ) 52 / 64",
"output": [
"a"
]
},
{
"id": "task1424-66cc85fd7183452bbda6949e23a820bb",
"input": "Problem: two letters from the word khantkar are selected at random . what is the probability that at least one of the selected letters is a consonant ? \nOptions: a ) 25 / 28 , b ) 27 / 28 , c ) 30 / 28 , d ) 40 / 28 , e ) 50 / 28",
"output": [
"b"
]
},
{
"id": "task1424-658cfeb3f98a4f6cae649d6e34583d62",
"input": "Problem: in how many ways 4 boys and 4 girls can be seated in a row so that boys and girls are alternate ? \nOptions: a ) 1152 , b ) 1987 , c ) 2012 , d ) 1856 , e ) 2546",
"output": [
"a"
]
},
{
"id": "task1424-25d345a5fbe64f6b9dcd2ccdc947b998",
"input": "Problem: a bag contains 6 black and 9 white balls . one ball is drawn at random . what is the probability that the ball drawn is white ? \nOptions: a ) 4 , b ) 4 / 3 , c ) 4 / 5 , d ) 4 / 9 , e ) 3 / 5",
"output": [
"e"
]
},
{
"id": "task1424-ebec7976bb2948d9a3aae4383c9514e6",
"input": "Problem: in how many ways 6 boys and 4 girls can be seated in a row so that they are alternative ? \nOptions: a ) 14420 , b ) 12620 , c ) 17280 , d ) 21200 , e ) 24560",
"output": [
"c"
]
},
{
"id": "task1424-c2def70fad7249d5baa764beb0696e73",
"input": "Problem: a bag contains 3 red , 4 black and 2 white balls . what is the probability of drawing a red and a white ball in two successive draws , each ball being put back after it is drawn ? \nOptions: a ) 2 / 27 , b ) 1 / 9 , c ) 1 / 3 , d ) 4 / 27 , e ) 2 / 9",
"output": [
"d"
]
},
{
"id": "task1424-74ca1837ff4d4a7d9c667a89d307be04",
"input": "Problem: when two dice are tossed , what is the probability that the total score is a prime number ? \nOptions: a ) 1 / 6 , b ) 3 , c ) 5 / 12 , d ) 7 / 12 , e ) 9 / 12",
"output": [
"c"
]
},
{
"id": "task1424-a4ee722de2064de985fc006b23eaef9d",
"input": "Problem: there are 15 balls in a jar . you take out 3 blue balls without putting them back inside , and now the probability of pulling out a blue ball is 1 / 3 . how many blue balls were there in the beginning ? \nOptions: a ) 12 . , b ) 9 . , c ) 8 . , d ) 7 . , e ) 6 .",
"output": [
"d"
]
},
{
"id": "task1424-a6979699d947434cba9a0d3fe3df78c8",
"input": "Problem: in how many ways 3 boys and 3 girls can be seated in a row so that boys and girls are alternate ? \nOptions: a ) 69 , b ) 70 , c ) 71 , d ) 72 , e ) 73",
"output": [
"d"
]
},
{
"id": "task1424-03096081a2b54a608106425d42d2e76e",
"input": "Problem: a meeting has to be conducted with 5 managers . find the number of ways in which the managers may be selected from among 8 managers , if there are 2 managers who refuse to attend the meeting together . \nOptions: a ) 36 , b ) 40 , c ) 45 , d ) 51 , e ) 56",
"output": [
"a"
]
},
{
"id": "task1424-63b4f785fb1446e1a69ddf209196cdf8",
"input": "Problem: a box contains 25 electric bulbs , out of which 4 are defective . two bulbs are chosen at random from this box . the probability that at least one of these is defective is \nOptions: a ) 3 / 10 , b ) 7 / 19 , c ) 12 / 19 , d ) 21 / 95 , e ) none",
"output": [
"a"
]
},
{
"id": "task1424-65bc5d955f1549b4a86d134b3e247ce9",
"input": "Problem: what is the probability of getting exactly three heads on five flips of a fair coin ? \nOptions: a ) 1 / 32 , b ) 3 / 32 , c ) 1 / 4 , d ) 5 / 16 , e ) 1 / 2",
"output": [
"d"
]
},
{
"id": "task1424-7287c3109482409c84d2d1657081dbdd",
"input": "Problem: what is the probability that the sum of two dice will yield a 8 , and then when both are thrown again , their sum will again yield a 8 ? assume that each die has 7 sides with faces numbered 1 to 7 . \nOptions: a ) 1 / 144 , b ) 1 / 36 , c ) 1 / 12 , d ) 1 / 6 , e ) 1 / 49",
"output": [
"e"
]
},
{
"id": "task1424-d3c7fd2f16e945ef8aa54e376b4b98ca",
"input": "Problem: if x is to be chosen at random from the set { 1 , 2 , 3 , 4 } and y is to be chosen at random from the set { 5 , 6 , 7 } , what is the probability that xy will be odd ? \nOptions: a ) 1 / 6 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 6",
"output": [
"b"
]
},
{
"id": "task1424-ca4378f85b5c42dba919ff9d8ed005d3",
"input": "Problem: in a bag containing 3 balls , a white ball was placed and then 1 ball was taken out at random . what is the probability that the extracted ball would turn on to be white , if all possible hypothesis concerning the color of theballs that initiallyin the bag were equally possible ? \nOptions: a ) 2 / 3 , b ) 5 / 8 , c ) 5 / 9 , d ) 3 / 7 , e ) 4 / 7",
"output": [
"b"
]
},
{
"id": "task1424-aeb56c965e974993a391708d01f79bf0",
"input": "Problem: a string of 13 light bulbs is wired in such a way that if any individual light bulb fails , the entire string fails . if for each individual light bulb the probability of failing during time period t is 0.02 , what is the probability that the string of light bulbs will fail during the time period t ? \nOptions: a ) 0.02 , b ) ( 0.02 ) ^ 13 , c ) 1 - ( 0.02 ) ^ 13 , d ) ( 0.98 ) ^ 13 , e ) 1 - ( 0.98 ) ^ 13",
"output": [
"e"
]
},
{
"id": "task1424-b1dd2032efd54c81a12181defa3dd176",
"input": "Problem: tom and marry each have a bag of marbles , each of which contains 4 red marbles , 10 blue marbles , and 6 yellow marbles . if tom and marry each select one marble from their respective bags , what is the probability that either tom or marry select a blue marble ? \nOptions: a ) 1 / 7 , b ) 2 / 4 , c ) 3 / 4 , d ) 1 / 8 , e ) 1 / 16",
"output": [
"c"
]
},
{
"id": "task1424-01a24bd778f74f349cf2bd98109aecfd",
"input": "Problem: what is the probability of randomly selecting one of the shortest diagonals from all the diagonals of a regular 11 - sided polygon ) ? \nOptions: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 8 , e ) 1 / 11",
"output": [
"c"
]
},
{
"id": "task1424-7d21afd22473419c9db3d928e368d7f5",
"input": "Problem: there are 21 students in a class . in how many different ways can a committee of 3 students be formed ? \nOptions: a ) 1180 , b ) 1330 , c ) 1540 , d ) 1760 , e ) 1920",
"output": [
"b"
]
},
{
"id": "task1424-faab4bfa40c4458c8e9fdc6be303f9f1",
"input": "Problem: there are 7 pairs of socks and 2 socks are worn from that such that the pair of socks worn are not of the same pair . what is the number of pair that can be formed . \nOptions: a ) 40 , b ) 49 , c ) 41 , d ) 56 , e ) 42",
"output": [
"e"
]
},
{
"id": "task1424-2189db131a08442ebb812f4486c3bb21",
"input": "Problem: in a lottery there are 10 prizes and 25 blanks . a lottery is drawn at random . what is the probability of getting a prize ? \nOptions: a ) 1 / 5 , b ) 2 / 7 , c ) 2 / 5 , d ) 1 / 7 , e ) 3 / 5",
"output": [
"b"
]
},
{
"id": "task1424-08e968ec13df4c65aeb24666c3acc43e",
"input": "Problem: when fair coin is tossed 9 times find the probability of getting head at least once . \nOptions: a ) 1 / 512 , b ) 511 / 512 , c ) 9 / 512 , d ) 503 / 51 , e ) 503 / 510",
"output": [
"b"
]
},
{
"id": "task1424-80f8432caf9445e8a2cb878bc9171302",
"input": "Problem: how many different ways can 2 students be seated in a row of 7 desks , so that there is always at least one empty desk between the students ? \nOptions: a ) 2 , b ) 3 , c ) 30 , d ) 6 , e ) 12",
"output": [
"c"
]
},
{
"id": "task1424-4c17b181126345e4b25805c970c56a92",
"input": "Problem: jane and thomas are among the 7 people from which a committee of 3 people is to be selected . how many different possible committees of 3 people can be selected from these 7 people if at least one of either jane or thomas is to be selected ? \nOptions: a ) 20 , b ) 25 , c ) 30 , d ) 35 , e ) 40",
"output": [
"b"
]
},
{
"id": "task1424-3774b414681c42f9a251e5163aea1c3e",
"input": "Problem: a box contains 23 electric bulbs , out of which 4 are defective . two bulbs are chosen at random from this box . the probability that at least one of these is defective is \nOptions: a ) 4 / 19 , b ) 7 / 19 , c ) 12 / 37 , d ) 21 / 95 , e ) none",
"output": [
"c"
]
},
{
"id": "task1424-a7773c09fe3b49ad827deab5beeb1067",
"input": "Problem: how many different pairs of numbers ( s , t ) such that s = 3 t can be obtained if s and t are selected from the set of number { 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 } \nOptions: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5",
"output": [
"e"
]
},
{
"id": "task1424-970d22b0e674403b98e3ccec20ca53b0",
"input": "Problem: a certain club has 10 members , including jarry . one of the 10 members is chosen at random to be the president , one of the remaining 9 members is to be chosen at random to be the secretary , and one of the remaining 8 members is to be chosen at random to be the treasurer . what is the probability that jarry will be either the member chose to be secretary or the member chose to be treasurer ? \nOptions: a ) 1 / 720 , b ) 1 / 80 , c ) 1 / 10 , d ) 1 / 9 , e ) 1 / 5",
"output": [
"e"
]
},
{
"id": "task1424-28b4f84eff014dea89d591cf885098ef",
"input": "Problem: what is the probability of randomly selecting one of the shortest diagonals from all the diagonals of a regular decagon ( 10 - sided polygon ) ? \nOptions: a ) 3 / 10 , b ) 2 / 5 , c ) 2 / 7 , d ) 10 / 21 , e ) 5 / 11",
"output": [
"c"
]
},
{
"id": "task1424-3ab114fc8c48479b80c8834e70676e8d",
"input": "Problem: the main line train starts at 5.00 am and the harbor line train starts at 5.02 am . each train has the frequency of 10 minutes . if a guy goes in the morning at a random time what is the probability of he getting main line train ? \nOptions: a ) . 5 , b ) 0.6 , c ) 0.4 , d ) 0.7 , e ) 0.8",
"output": [
"e"
]
},
{
"id": "task1424-f925e146dc7b44a7b4bf03c4b6019d6d",
"input": "Problem: a bag contains 15 red jellybeans and 15 blue jellybeans . if 3 jellybeans are removed one at a time , at random and are not replaced , what is the probability that all 3 jellybeans removed from the bag are blue ? \nOptions: a ) 9 / 100 , b ) 2 / 19 , c ) 1 / 8 , d ) 3 / 20 , e ) 3 / 10",
"output": [
"e"
]
},
{
"id": "task1424-0562bf237cc74b98bfb03b6ea072c28e",
"input": "Problem: in how many ways 7 boys and 7 girls can be seated in a row so that boys and girls are alternate ? \nOptions: a ) 50803200 , b ) 50328000 , c ) 50003280 , d ) 50703200 , e ) 50603200",
"output": [
"a"
]
},
{
"id": "task1424-0f1fb0f80f764c9195ae5fd5d1807d96",
"input": "Problem: what is the probability of getting exactly 1 head in a single throw of five fair coins ? \nOptions: a ) 1 / 4 , b ) 3 / 8 , c ) 3 / 16 , d ) 5 / 32 , e ) 7 / 32",
"output": [
"d"
]
},
{
"id": "task1424-dab8799ecde1436b9c41462e84545d11",
"input": "Problem: from a pack of cards , two cards are drawn one after the other , with replacement . what is the probability that the first card is a black card and the second card is a king ? \nOptions: a ) 1 / 26 , b ) 1 / 13 , c ) 3 / 52 , d ) 3 / 26 , e ) 15 / 26",
"output": [
"a"
]
},
{
"id": "task1424-5579ab6412b94b4b9e100f83a1ef66a2",
"input": "Problem: what is the probability of randomly selecting one of the shortest diagonals from all the diagonals of a regular 7 - sided polygon ) ? \nOptions: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 6 , e ) 1 / 7",
"output": [
"a"
]
},
{
"id": "task1424-d4cf15f721e34a759b3eb54abbf22d14",
"input": "Problem: two unbiased coins are tossed . find the probability of getting two heads ? \nOptions: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 2 / 3 , e ) 3 / 5",
"output": [
"c"
]
},
{
"id": "task1424-82431d5ae2204d2ca6e5a6e2fb4402bd",
"input": "Problem: if 2 cards are selected at random from the deck of 52 cards then what is the probability of one of the selected cards will be king and other will be 10 ? a deck of cards has a total of 52 cards , consisting of 4 suits ; ( spades ( black ) , hearts ( red ) , diamond ( red ) s , and clubs ( black ) ) ; and 13 cards including 1 king , 1 queen and 1 jack in each suit \nOptions: a ) 8 / 2652 , b ) 18 / 2652 , c ) 1 / 2652 , d ) 12 / 2652 , e ) 16 / 2652",
"output": [
"b"
]
},
{
"id": "task1424-e10381cc4795403ab9f91a09f5fda9d0",
"input": "Problem: four 6 faced dice are thrown together . the probability that all the three show the same number on them is ? \nOptions: a ) 1 / 32 , b ) 1 / 216 , c ) 1 / 33 , d ) 1 / 38 , e ) 1 / 34",
"output": [
"b"
]
},
{
"id": "task1424-4f2631e285ee4957ac25d07c3e7d25df",
"input": "Problem: there are 6 books on a shelf , of which 2 are paperbacks and 4 are hardbacks . how many possible selections of 4 books from this shelf include at least one paperback ? \nOptions: a ) a ) 40 , b ) b ) 14 , c ) c ) 50 , d ) d ) 55 , e ) e ) 60",
"output": [
"b"
]
},
{
"id": "task1424-7865a86decdd4c6b93d162298db6c517",
"input": "Problem: there is a 30 % chance sandy will visit china this year , while there is a 60 % chance that she will visit malaysia this year . what is the probability that sandy will visit either china or malaysia this year , but not both ? \nOptions: a ) 42 % , b ) 48 % , c ) 54 % , d ) 60 % , e ) 66 %",
"output": [
"c"
]
},
{
"id": "task1424-916879b4b04d464abb4f71db60d4bb2a",
"input": "Problem: a bag contains 6 red , 3 yellow and 4 green balls . 3 balls are drawn randomly . what is the probability that the balls drawn contain balls of different colours ? \nOptions: a ) 2 / 7 , b ) 3 / 5 , c ) 3 / 11 , d ) 1 / 4 , e ) 7 / 16",
"output": [
"d"
]
},
{
"id": "task1424-84f1104b5d964d2c88d8e5b9ab38c1dd",
"input": "Problem: a store has 10 bottles of juice , including 5 bottles of apple juice . in the evening , 6 bottles of juice are sold one by one . what is the probability of selling 4 bottles of apple juice among the 6 bottles ? assume that every bottle has an equal chance of being bought . \nOptions: a ) 2 / 7 , b ) 3 / 11 , c ) 4 / 15 , d ) 5 / 21 , e ) 6 / 25",
"output": [
"d"
]
},
{
"id": "task1424-677d5aa405144f93bfa60516aca8488f",
"input": "Problem: how many cubes of 8 cm edge can be cut out of a cube of 16 cm edge \nOptions: a ) 36 , b ) 2 , c ) 8 , d ) 48 , e ) none of these",
"output": [
"c"
]
},
{
"id": "task1424-90fdcabfbd224ea381b8d86885ca85ff",
"input": "Problem: there are 18 balls in a jar . you take out 3 blue balls without putting them back inside , and now the probability of pulling out a blue ball is 1 / 5 . how many blue balls were there in the beginning ? \nOptions: a ) 12 , b ) 9 , c ) 8 , d ) 7 , e ) 6",
"output": [
"e"
]
},
{
"id": "task1424-8dd4a42ad55f476bb22e2efe5ce6b4ba",
"input": "Problem: a question paper has 2 parts , a & b , each containing 6 questions . if a student has to choose 4 from part a & 3 from part b , in how many ways can he choose the questions ? \nOptions: a ) 100 , b ) 200 , c ) 350 , d ) 150 , e ) 140",
"output": [
"d"
]
},
{
"id": "task1424-aebaac0312ec4241be0068dc56f88252",
"input": "Problem: what is the probability of getting atmost one head when two unbiased coin are tossed ? \nOptions: a ) 3 / 4 , b ) 3 / 2 , c ) 4 / 3 , d ) 1 / 2 , e ) 2 / 6",
"output": [
"a"
]
},
{
"id": "task1424-0da9a6db9d5948f7896d762484f308a4",
"input": "Problem: three unbiased coins are tossed , what is the probability of ge ƫ ng at least 2 tails ? \nOptions: a ) 1 / 3 , b ) 1 / 6 , c ) 1 / 2 , d ) 1 / 8 , e ) none of these",
"output": [
"c"
]
},
{
"id": "task1424-ebdbfe35ae874488b5bf845f0a6bbc17",
"input": "Problem: three coins are tossed . find the probability of at least 1 head and 1 tail ? \nOptions: a ) 1 / 2 , b ) 1 / 4 , c ) 3 / 4 , d ) 7 / 8 , e ) 1 / 8",
"output": [
"c"
]
},
{
"id": "task1424-fe22ed2b6745401b9315180d3bd6303c",
"input": "Problem: when tossed , a certain coin has equal probability of landing on either side . if the coin is tossed 4 times , what is the probability that it will land on the same side each time ? \nOptions: a ) 1 / 8 , b ) 1 / 4 , c ) 1 / 16 , d ) 1 / 2 , e ) 1 / 32",
"output": [
"a"
]
},
{
"id": "task1424-8bffbbdb5cae43608fc7f2555d53766f",
"input": "Problem: a bag contains 30 red jellybeans and 30 blue jellybeans . if 3 jellybeans are removed one at a time , at random and are not replaced , what is the probability that all 3 jellybeans removed from the bag are blue ? \nOptions: a ) 9 / 100 , b ) 2 / 19 , c ) 1 / 8 , d ) 1 / 20 , e ) 3 / 10",
"output": [
"d"
]
},
{
"id": "task1424-c499238e750949f3b464c2c5df497fc4",
"input": "Problem: 3 houses are available in a new flat . 3 persons apply for the houses . each applies for 1 house without consulting others . the probability that all the 3 apply for the same house is ? \nOptions: a ) 1 / 7 , b ) 1 / 9 , c ) 2 / 7 , d ) 3 / 7 , e ) 2 / 9",
"output": [
"b"
]
},
{
"id": "task1424-9c0a6cf6261f4576a44962795f998f9d",
"input": "Problem: two dice are thrown simultaneously . what is the probability of getting two numbers whose product is not an even ? \nOptions: a ) 1 / 2 , b ) 1 / 4 , c ) 2 / 3 , d ) 2 / 5 , e ) 3 / 7",
"output": [
"b"
]
},
{
"id": "task1424-407289db38ef4211a1011409c575b67b",
"input": "Problem: find the probability that a non leap year selected at random will have 53 sundays \nOptions: a ) 6 / 7 , b ) 5 / 7 , c ) 4 / 7 , d ) 3 / 7 , e ) 1 / 7",
"output": [
"e"
]
},
{
"id": "task1424-e2f7828dbfec43469471378f42998127",
"input": "Problem: from a pack of 52 cards , 1 card is drawn at random . what is the probability that a red card is drawn ? \nOptions: a ) 1 / 2 , b ) 1 / 4 , c ) 1 / 26 , d ) 1 / 13 , e ) 5 / 13",
"output": [
"a"
]
},
{
"id": "task1424-dfae84fd773d40ffa62eab27850b5888",
"input": "Problem: a question paper has 2 parts , a & b , each containing 7 questions . if a student has to choose 5 from part a & 4 from part b , in how many ways can he choose the questions ? \nOptions: a ) 1100 , b ) 1200 , c ) 1235 , d ) 1354 , e ) 735",
"output": [
"e"
]
},
{
"id": "task1424-e62eff574998401ba8424c57cc43252c",
"input": "Problem: a meeting has to be conducted with 3 managers . find the number of ways in which the managers be selected from among 6 managers , if 2 managers will not attend the meeting together ? \nOptions: a ) 18 , b ) 20 , c ) 16 , d ) 22 , e ) 24",
"output": [
"c"
]
},
{
"id": "task1424-91ed42d8aac4405aa201674681feb592",
"input": "Problem: in a single throw of a die , what is probability of getting a number greater than 4 ? \nOptions: a ) 2 / 3 , b ) 3 / 5 , c ) 4 / 7 , d ) 8 / 9 , e ) 1 / 3",
"output": [
"e"
]
},
{
"id": "task1424-697e609d5d2941d38f58d34133190a2f",
"input": "Problem: there are 15 boys and 10 girls in a class . if three students are selected at random , in how many ways that 1 girl and 2 boys are selected ? \nOptions: a ) 950 , b ) 1050 , c ) 2150 , d ) 2050 , e ) 1000",
"output": [
"b"
]
},
{
"id": "task1424-7804f11a74ac45fdb2a9b17c69767b8c",
"input": "Problem: a certain junior class has 1,000 students and a certain senior class has 400 students . among these students , there are 60 siblings pairs , each consisting of 1 junior and 1 senior . if 1 student is to be selected at random from each class , what is the probability that the 2 students selected at will be a sibling pair ? \nOptions: a ) 3 / 20,000 , b ) 1 / 3,600 , c ) 9 / 2,000 , d ) 1 / 60 , e ) 1 / 15",
"output": [
"a"
]
},
{
"id": "task1424-baadb155aa1648d28f02181566ee2b32",
"input": "Problem: in a garden , there are yellow and green flowers which are straight and curved . if the probability of picking a green flower is 1 / 5 and picking a straight flower is 1 / 2 , then what is the probability of picking a flower which is yellow and straight \nOptions: a ) 1 / 7 , b ) 1 / 8 , c ) 2 / 5 , d ) 3 / 4 , e ) 7 / 8",
"output": [
"c"
]
},
{
"id": "task1424-a426e854900642698c3ddf3b00501ff3",
"input": "Problem: a coin is tossed 4 times . what is the probability of getting exactly 3 heads ? \nOptions: a ) 1 / 2 , b ) 1 / 4 , c ) 1 / 8 , d ) 1 / 16 , e ) 3 / 16",
"output": [
"b"
]
},
{
"id": "task1424-9f77abb286d04781bef971c8c1cd21f2",
"input": "Problem: 6 students are equally divided into 3 groups , then , the 3 groups were assigned to 3 different topics . how many different arrangements w are possible ? \nOptions: a ) 30 , b ) 60 , c ) 90 , d ) 180 , e ) 540",
"output": [
"c"
]
},
{
"id": "task1424-321aaff729f14e8d911ff1c139bb5f1f",
"input": "Problem: a certain junior class has 1000 students and a certain senior class has 600 students . among these students , there are 60 siblings pairs each consisting of 1 junior and 1 senior . if 1 student is to be selected at random from each class , what is the probability that the 2 students selected will be a sibling pair ? \nOptions: a ) 3 / 40000 , b ) 1 / 1000 , c ) 9 / 2000 , d ) 1 / 60 , e ) 1 / 15",
"output": [
"b"
]
},
{
"id": "task1424-9ee478a9614a41d999650e9c67b1d1c5",
"input": "Problem: there are 24 students in a class . in how many different ways can a committee of 3 students be formed ? \nOptions: a ) 1250 , b ) 1800 , c ) 2024 , d ) 3256 , e ) 2864",
"output": [
"c"
]
},
{
"id": "task1424-e8cb416a970c4cafac1241680e499049",
"input": "Problem: a man & his wife appear in an interview for 2 vacancies in the same post . the probability of husband ' s selection is 1 / 7 & the probability of wife ' s selection is 1 / 5 . what is the probability that only 1 of them is selected ? \nOptions: a ) 1 / 3 , b ) 2 / 3 , c ) 2 / 7 , d ) 3 / 11 , e ) 4 / 5",
"output": [
"c"
]
},
{
"id": "task1424-b83549838c1348ad9a9f86b32bfe51fe",
"input": "Problem: what is the probability that the sum of two dice will yield a 9 , and then when both are thrown again , their sum will again yield a 9 ? assume that each die has 8 sides with faces numbered 1 to 8 . \nOptions: a ) 1 / 64 , b ) 1 / 36 , c ) 1 / 12 , d ) 1 / 6 , e ) 1 / 3",
"output": [
"a"
]
}
],
"Instance License": [
"Apache 2.0"
]
}
Reference in New Issue View Git Blame Copy Permalink