{ "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" ] }