niryuu/sni-each-converted huggingface dataset:
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 ? 
Options: a ) 3 / 4 , b ) 2 / 5 , c ) 1 / 7 , d ) 1 / 8 , e ) 4 / 3
Output: b
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 ? 
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 12
Output: d
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 ? 
Options: a ) 50 , b ) 100 , c ) 152 , d ) 150 , e ) 55
Output: a
Problem: seven 6 faced dice are thrown together . the probability that all the three show the same number on them is ? 
Options: a ) 1 / 32 , b ) 1 / 46656 , c ) 1 / 33 , d ) 1 / 38 , e ) 1 / 34
Output: b
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 ? 
Options: a ) 6600 , b ) 1300 , c ) 6780 , d ) 1976 , e ) 2448
Output: a
Problem: how many cubes of 5 cm edge can be cut out of a cube of 15 cm edge 
Options: a ) 36 , b ) 232 , c ) 27 , d ) 48 , e ) none of these
Output: c
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 . 
Options: a ) 62 , b ) 70 , c ) 72 , d ) 71 , e ) 76
Output: c
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 ? 
Options: a ) 1 / 5 , b ) 1 / 10 , c ) 1 / 12 , d ) 1 / 16 , e ) 1 / 32
Output: d
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 ? 
Options: a ) 1100 , b ) 1200 , c ) 1235 , d ) 1354 , e ) 1140
Output: e
Problem: if two integers x , y ( x > y ) are selected from - 10 to 10 ( inclusive ) , how many possible cases are there ? 
Options: a ) 150 , b ) 180 , c ) 190 , d ) 210 , e ) 240
Output: d
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 ? 
Options: a ) 61 , b ) 78 , c ) 71 , d ) 68 , e ) 94
Output: c
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 ? 
Options: a ) 2 , b ) 3 , c ) 4 , d ) 20 , e ) 12
Output: d
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 ? 
Options: a ) 10 / 40 , b ) 12 / 40 , c ) 8 / 40 , d ) 3 / 40 , e ) 7 / 40
Output: b
Problem: two unbiased coins are tossed . what is the probability of getting two heads ? 
Options: a ) 1 / 2 , b ) 1 / 4 , c ) 2 / 3 , d ) 1 / 5 , e ) 2 / 7
Output: b
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 ? 
Options: a ) 15 / 56 , b ) 41 / 56 , c ) 13 / 28 , d ) 15 / 28 , e ) 5 / 14
Output: d
Problem: if a card is drawn from a well shuffled pack of cards , the probability of drawing a spade or a king is ? 
Options: a ) 4 / 15 , b ) 4 / 10 , c ) 4 / 18 , d ) 4 / 13 , e ) 4 / 11
Output: d
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 ? 
Options: a ) 1 / 2 , b ) 1 / 4 , c ) 1 / 8 , d ) 1 / 16 , e ) 1 / 32
Output: e
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 ? 
Options: a ) 21 / 40 , b ) 2 / 5 , c ) 7 / 15 , d ) 4 / 15 , e ) 11 / 30
Output: a
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 ? 
Options: a ) 17 / 30 , b ) 2 / 5 , c ) 7 / 15 , d ) 8 / 15 , e ) 11 / 30
Output: d
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 ? 
Options: a ) 88 , b ) 90 , c ) 92 , d ) 96 , e ) 98
Output: a
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 ? 
Options: a ) 1 / 10 , b ) 4 / 9 , c ) 1 / 2 , d ) 9 / 15 , e ) 2 / 3
Output: d
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 ? 
Options: a ) 2 / 9 , b ) 3 / 8 , c ) 2 / 7 , d ) 1 / 6 , e ) 1 / 5
Output: e
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 . 
Options: a ) 1 / 7 , b ) 1 / 12 , c ) 1 / 14 , d ) 1 / 18 , e ) 1 / 21
Output: c
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 ? 
Options: a ) 28 , b ) 46 , c ) 55 , d ) 63 , e ) 70
Output: c
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 ? 
Options: a ) 15 / 56 , b ) 41 / 56 , c ) 13 / 28 , d ) 15 / 28 , e ) 5 / 14
Output: d
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 ? 
Options: a ) 12 . , b ) 9 . , c ) 8 . , d ) 7 . , e ) 6 .
Output: b
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 . 
Options: a ) 36 , b ) 40 , c ) 42 , d ) 45 , e ) 49
Output: e
Problem: a card is drawn from a pack of 52 cards . the probability of not getting a face card ? 
Options: a ) 9 / 13 , b ) 5 / 12 , c ) 3 / 13 , d ) 6 / 17 , e ) 1 / 13
Output: a
Problem: in a single throw of a die , what is the probability of getting a number greater than 2 ? 
Options: a ) 1 / 2 , b ) 2 / 5 , c ) 1 / 3 , d ) 2 / 7 , e ) 2 / 3
Output: e
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 ? 
Options: a ) 15 / 56 , b ) 41 / 56 , c ) 13 / 28 , d ) 15 / 28 , e ) 5 / 14
Output: d
Problem: 4 dices are thrown at the same time . what is the probability of getting only 2 dices showing the same face ? 
Options: a ) 4 / 9 , b ) 5 / 9 , c ) 11 / 18 , d ) 7 / 9 , e ) none of the above
Output: b
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 ? 
Options: a ) 1 / 5 , b ) 3 / 20 , c ) 1 / 7 , d ) 2 / 15 , e ) 3 / 28
Output: e
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 . 
Options: a ) 48 , b ) 55 , c ) 58 , d ) 62 , e ) 70
Output: b
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 ? 
Options: a ) 2 / 3 , b ) 1 / 3 , c ) 2 / 9 , d ) 1 / 12 , e ) 1 / 24
Output: d
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 ? 
Options: a ) 2 / 25 , b ) 1 / 50 , c ) 1 / 12 , d ) 1 / 6 , e ) 1 / 3
Output: e
Problem: what is the probability of getting a number less than 4 when a die is rolled ? 
Options: a ) 5 / 5 , b ) 1 / 2 , c ) 5 / 1 , d ) 5 / 7 , e ) 5 / 2
Output: b
Problem: what is the probability of randomly selecting one of the shortest diagonals from all the diagonals of a regular octagon ? 
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 5 , e ) 7 / 8
Output: d
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 ? 
Options: a ) 1 / 13 , b ) 1 / 20 , c ) 1 / 26 , d ) 1 / 50 , e ) 1 / 100
Output: c
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 . 
Options: a ) 1 , b ) 159 / 160 , c ) 157 / 160 , d ) 4 3 / 160 , e ) 0
Output: c
Problem: if two dice are thrown together , the probability of getting an even prime number on the dice is 
Options: a ) 1 / 36 , b ) 1 / 18 , c ) 1 / 13 , d ) 1 / 9 , e ) 5 / 36
Output: a
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 ? 
Options: a ) 51 / 145 , b ) 9 / 25 , c ) 3 / 5 , d ) 94 / 145 , e ) 5 / 6
Output: a
Problem: what is the probability of getting sum 10 with the help of three dice ? 
Options: a ) 1 / 4 , b ) 1 / 8 , c ) 1 / 16 , d ) 1 / 24 , e ) 1 / 32
Output: b
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 
Options: a ) 1 / 6 , b ) 1 / 8 , c ) 1 / 4 , d ) 3 / 4 , e ) 7 / 8
Output: a
Problem: three unbiased coins are tossed , what is the probability of getting at least 2 tails ? 
Options: a ) 1 / 5 , b ) 1 / 7 , c ) 1 / 8 , d ) 1 / 2 , e ) 1 / 10
Output: d
Problem: how many positive integers less than 600 can be formed using the numbers 1 , 2 , 3 , 5 and 6 for the digits ? 
Options: a ) 48 , b ) 130 , c ) 66 , d ) 68 , e ) 84
Output: b
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 ? 
Options: a ) 1 / 8 , b ) 1 / 16 , c ) 1 / 32 , d ) 1 / 64 , e ) 1 / 128
Output: d
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 ? 
Options: a ) 5 / 8 , b ) 5 / 6 , c ) 5 / 1 , d ) 5 / 9 , e ) 5 / 2
Output: d
Problem: there are 23 students in a class . in how many different ways can a committee of 3 students be formed ? 
Options: a ) 1254 , b ) 1482 , c ) 1771 , d ) 1875 , e ) 1923
Output: c
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 ? 
Options: a ) 1 / 20 , b ) 3 / 40 , c ) 13 / 40 , d ) 7 / 10 , e ) 13 / 22
Output: d
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 ? 
Options: a ) 3 / 5 , b ) 5 / 8 , c ) 6 / 7 , d ) 7 / 8 , e ) 6 / 7
Output: b
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 ? 
Options: a ) 1 / 2 , b ) 1 / 4 , c ) 1 / 8 , d ) 1 / 16 , e ) 1 / 32
Output: e
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 ? 
Options: a ) 1 / 33 , b ) 2 / 33 , c ) 1 / 3 , d ) 16 / 33 , e ) 8 / 21
Output: e
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 ? 
Options: a ) 0.75 , b ) 1 , c ) 0.25 , d ) 0.5 , e ) 0.58
Output: c
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 ? 
Options: a ) 20 % , b ) 25 % , c ) 40 % , d ) 60 % , e ) 75 %
Output: b
Problem: three 8 faced dice are thrown together . the probability that all the three show the same number on them is ? 
Options: a ) 1 / 38 , b ) 1 / 48 , c ) 1 / 56 , d ) 1 / 64 , e ) 1 / 68
Output: d
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 ? 
Options: a ) 10 / 45 , b ) 14 / 45 , c ) 8 / 45 , d ) 3 / 45 , e ) 7 / 45
Output: b
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 ? 
Options: a ) 2 / 5 , b ) 11 / 5 , c ) 1 / 9 , d ) 1 / 17 , e ) 1 / 5
Output: d
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 ? 
Options: a ) 15 / 64 , b ) 30 / 64 , c ) 1 / 2 , d ) 1 / 4 , e ) 52 / 64
Output: a
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 ? 
Options: a ) 10 / 35 , b ) 11 / 35 , c ) 8 / 35 , d ) 3 / 35 , e ) 7 / 35
Output: b
Problem: a fair coin is tossed 15 times . what is the probability of getting more heads than tails in 15 tosses ? 
Options: a ) 1 / 2 , b ) 63 / 128 , c ) 4 / 7 , d ) 61 / 256 , e ) 63 / 64
Output: a
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 ? 
Options: a ) 1 / 13 , b ) 1 / 15 , c ) 11 / 9 , d ) 1 / 10 , e ) 1 / 25
Output: a
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 ? 
Options: a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 5 / 22
Output: b
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 ? 
Options: a ) 3 / 40000 , b ) 2 / 30000 , c ) 9 / 2000 , d ) 1 / 60 , e ) 1 / 15
Output: b
Problem: three unbiased coins are tossed . what is the probability of getting at least 2 heads ? 
Options: a ) 1 / 4 , b ) 1 / 2 , c ) 1 / 3 , d ) 1 / 8 , e ) 1 / 6
Output: b
Problem: there are 4 red shoes & 4 green shoes . if two of red shoes are drawn what is the probability of getting red shoes 
Options: a ) 1 / 3 , b ) 1 / 14 , c ) 3 / 14 , d ) 1 / 15 , e ) 1 / 16
Output: c
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 . 
Options: a ) 34 , b ) 677 , c ) 197 , d ) 177 , e ) 191
Output: a
Problem: when two dice are rolled , what is the probability that the sum of the two numbers is 6 ? 
Options: a ) 1 / 9 , b ) 5 / 36 , c ) 1 / 3 , d ) 2 / 36 , e ) none of the above
Output: b
Problem: three unbiased coins are tossed . what is the probability of getting 1 heads , 1 tail ? 
Options: a ) 3 / 4 , b ) 1 / 4 , c ) 3 / 8 , d ) 7 / 8 , e ) 2 / 8
Output: e
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 
Options: a ) 1 / 13 , b ) 2 / 13 , c ) 1 / 26 , d ) 1 / 52 , e ) none of these
Output: c
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 . 
Options: a ) 18 , b ) 21 , c ) 25 , d ) 30 , e ) 35
Output: c
Problem: when two dice are rolled , what is the probability that the sum is either 7 or 11 ? 
Options: a ) 1 / 4 , b ) 1 / 9 , c ) 4 / 3 , d ) 3 / 9 , e ) 2 / 9
Output: e
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 ? 
Options: a ) 2 / 13 , b ) 1 / 26 , c ) 5 / 26 , d ) 1 / 52 , e ) 17 / 52
Output: d
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 ? 
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 5 , e ) 1 / 6
Output: a
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 ? 
Options: a ) 1 / 969 , b ) 2 / 969 , c ) 4 / 969 , d ) 5 / 323 , e ) 21 / 789
Output: d
Problem: what is the probability of getting a sum 9 from two throws of dice 
Options: a ) 1 / 3 , b ) 1 / 9 , c ) 1 / 12 , d ) 2 / 9 , e ) none of these
Output: b
Problem: two unbiased coins are tossed . find the probability of getting at most one head ? 
Options: a ) 1 / 2 , b ) 3 / 4 , c ) 2 / 5 , d ) 2 / 3 , e ) 1 / 4
Output: b
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 ? 
Options: a ) 3 / 4 , b ) 1 / 2 , c ) 1 / 7 , d ) 1 / 8 , e ) 4 / 3
Output: b
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 ? 
Options: a ) 2 / 3 , b ) 1 / 12 , c ) 2 / 9 , d ) 1 / 2 , e ) 1 / 24
Output: b
Problem: what is the probability of randomly selecting one of the shortest diagonals from all the diagonals of a regular hexagon ? 
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 7 / 9
Output: d
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 ? 
Options: a ) 35 , b ) 91 , c ) 120 , d ) 126 , e ) 150
Output: b
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 ? 
Options: a ) 2 / 3 , b ) 1 / 3 , c ) 2 / 9 , d ) 1 / 12 , e ) 1 / 24
Output: d
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 ? 
Options: a ) 219 , b ) 246 , c ) 252 , d ) 262 , e ) 270
Output: a
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 : 
Options: a ) 1 / 26 , b ) 1 / 52 , c ) 2 / 62 , d ) 2 / 26 , e ) 3 / 26
Output: a
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 ? 
Options: a ) 3 / 40,000 , b ) 1 / 10,000 , c ) 9 / 2,000 , d ) 1 / 60 , e ) 1 / 15
Output: b
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 ? 
Options: a ) 15 / 64 , b ) 30 / 64 , c ) 1 / 2 , d ) 1 / 4 , e ) 52 / 64
Output: a
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 ? 
Options: a ) 9 / 100 , b ) 2 / 19 , c ) 1 / 8 , d ) 3 / 20 , e ) 3 / 10
Output: b
Problem: in how many ways 4 boys and 4 girls can be seated in a row so that they are alternate . 
Options: a ) 144 , b ) 288 , c ) 12 , d ) 576 , e ) none
Output: d
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 ? 
Options: a ) 7 / 10 , b ) 2 / 4 , c ) 1 / 4 , d ) 1 / 8 , e ) 1 / 16
Output: a
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 ? 
Options: a ) 40 , b ) 46 , c ) 52 , d ) 62 , e ) 85
Output: e
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 ? 
Options: a ) 340 , b ) 346 , c ) 352 , d ) 365 , e ) 370
Output: d
Problem: if a card is drawn from a well shuffled pack of cards , the probability of drawing a spade or a king is - . 
Options: a ) 2 / 10 , b ) 4 / 13 , c ) 3 / 5 , d ) 9 / 7 , e ) 1 / 4
Output: b
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 ? 
Options: a ) 24 , b ) 120 , c ) 625 , d ) 720 , e ) 1024
Output: c
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 ? 
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 5 , d ) 4 / 7 , e ) 5 / 9
Output: d
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 ? . 
Options: a ) 5 / 42 , b ) 2 / 42 , c ) 7 / 42 , d ) 2 / 7 , e ) 5 / 7
Output: b
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 ? 
Options: a ) 8 / 25 , b ) 11 / 24 , c ) 12 / 25 , d ) 12 / 25 , e ) 12 / 23
Output: d
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 ? 
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 4 , d ) 5 / 8 , e ) 11 / 16
Output: c
Problem: four dice are thrown simultaneously . find the probability that all of them show the same face . 
Options: a ) 1 / 216 , b ) 1 / 215 , c ) 5 / 300 , d ) 1 / 415 , e ) 1 / 500
Output: a
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 ? 
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 5 , e ) 1 / 6
Output: c
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 ? 
Options: a ) 1 / 23445 , b ) 113 / 22434 , c ) 29187 by 1017926 , d ) 1017926 / 29187 , e ) none of these
Output: c
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 ? 
Options: a ) 0.125 , b ) 0.25 , c ) 0.75 , d ) 0.375 , e ) 0.666
Output: d
Problem: two dice are thrown simultaneously . what is the probability of getting two numbers whose product is even ? 
Options: a ) 1 / 2 , b ) 3 / 8 , c ) 3 / 4 , d ) 5 / 16 , e ) 9 / 16
Output: c
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 ? 
Options: a ) 2 / 7 , b ) 3 / 5 , c ) 3 / 11 , d ) 1 / 4 , e ) 7 / 16
Output: c
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 ? 
Options: a ) 55 % , b ) 60 % , c ) 70 % , d ) 72 % , e ) 80 %
Output: c
Problem: what is the probability of drawn an ace or a space or both from a dew of cards . 
Options: a ) 14 / 52 , b ) 15 / 52 , c ) 16 / 52 , d ) 17 / 52 , e ) 18 / 52
Output: c
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 ? 
Options: a ) 1 / 4 , b ) 1 / 2 , c ) 1 / 2 , d ) 2 , e ) 2 / 3
Output: d
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 ? 
Options: a ) 15 / 56 , b ) 41 / 56 , c ) 13 / 28 , d ) 15 / 28 , e ) 5 / 14
Output: d
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 : 
Options: a ) 29 / 34 , b ) 47 / 100 , c ) 3 / 20 , d ) 13 / 102 , e ) none of these
Output: d
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 ? 
Options: a ) 0.1 , b ) ( 0.1 ) ^ 30 , c ) 1 - ( 0.1 ) ^ 30 , d ) ( 0.93 ) ^ 30 , e ) 1 - ( 0.90 ) ^ 30
Output: e
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 ? 
Options: a ) 15 / 64 , b ) 30 / 64 , c ) 1 / 2 , d ) 1 / 4 , e ) 52 / 64
Output: a
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 ? 
Options: a ) 143 / 969 , b ) 134 / 969 , c ) 120 / 969 , d ) 19 / 969 , e ) 120 / 134
Output: b
Problem: three unbiased coins are tossed . what is the probability of getting 3 heads and 1 tail ? 
Options: a ) 3 / 4 , b ) 1 / 4 , c ) 3 / 8 , d ) 1 / 2 , e ) 1 / 8
Output: d
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 ? 
Options: a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 5 / 22
Output: e
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 . 
Options: a ) 2 / 25 , b ) 4 / 75 , c ) 7 / 75 , d ) 3 / 5 , e ) 4 / 45
Output: e
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 ? 
Options: a ) 0 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 1
Output: d
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 ? 
Options: a ) 3 / 5 , b ) 1 / 2 , c ) 1 / 5 , d ) 1 / 8 , e ) 1 / 32
Output: e
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 ? 
Options: a ) 1 / 3 , b ) 1 / 6 , c ) 5 / 12 , d ) 5 / 24 , e ) 7 / 24
Output: b
Problem: four 6 faced dice are thrown together . the probability that all the four show the same number on them is ? 
Options: a ) 1 / 248 , b ) 1 / 216 , c ) 1 / 144 , d ) 1 / 200 , e ) 1 / 242
Output: b
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 ? 
Options: a ) 9 / 100 , b ) 2 / 19 , c ) 1 / 8 , d ) 3 / 20 , e ) 3 / 10
Output: b
Problem: a fair coin is tossed 13 times . what is the probability of getting more heads than tails in 13 tosses ? 
Options: a ) 1 / 2 , b ) 63 / 128 , c ) 4 / 7 , d ) 61 / 256 , e ) 63 / 64
Output: a
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 ? 
Options: a ) 0.125 , b ) 0.375 , c ) 0.325 , d ) 0.5 , e ) 0.666
Output: b
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 ? 
Options: a ) 1 / 4 , b ) 1 / 2 , c ) 1 / 2 , d ) 5 / 8 , e ) 2 / 3
Output: c
Problem: a fair coin is tossed 3 times . what is the probability of getting at least 2 tails ? 
Options: a ) 3 / 4 , b ) 3 / 2 , c ) 1 / 2 , d ) 3 / 4 , e ) 1 / 4
Output: c
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 ? 
Options: a ) 1 / 52 , b ) 1 / 13 , c ) 1 / 26 , d ) 3 / 26 , e ) 17 / 26
Output: b
Problem: three 7 faced dice are thrown together . the probability that all the three show the same number on them is ? 
Options: a ) 1 / 38 , b ) 1 / 49 , c ) 1 / 39 , d ) 1 / 42 , e ) 1 / 29
Output: b
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 . 
Options: a ) 19 , b ) 20 , c ) 30 , d ) 32 , e ) 25
Output: b
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 ? 
Options: a ) 2 / 3 , b ) 1 / 3 , c ) 1 / 5 , d ) 5 / 42 , e ) 7 / 42
Output: d
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 ? 
Options: a ) 1 / 35 , b ) 1 / 10 , c ) 1 / 3 , d ) 1 / 462 , e ) 1 / 252
Output: d
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 ? 
Options: a ) 3 / 4 , b ) 3 / 8 , c ) 3 / 16 , d ) 5 / 16 , e ) 3 / 32
Output: b
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 ? 
Options: a ) 2 / 3 , b ) 2 / 5 , c ) 2 / 7 , d ) 2 / 9 , e ) 2 / 11
Output: d
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 ? 
Options: a ) 220 . , b ) 240 , c ) 260 , d ) 280 , e ) 300
Output: a
Problem: the odds in favour of an events are 3 : 5 . the probability of occurrence of the event is 
Options: a ) 3 / 8 , b ) 2 / 7 , c ) 1 / 3 , d ) 2 / 5 , e ) 6 / 7
Output: a
Problem: in a single throw of a die , what is the probability of getting a number greater than 4 ? 
Options: a ) 1 / 3 , b ) 1 / 4 , c ) 2 / 3 , d ) 2 / 5 , e ) 3 / 7
Output: a
Problem: a card is drawn from a pack of 52 cards . the probability of getting a queen club or a king of heart ? 
Options: a ) 3 / 26 , b ) 1 / 26 , c ) 4 / 26 , d ) 6 / 26 , e ) 10 / 26
Output: b
Problem: a card is drawn from a pack of 52 cards . the probability of getting a face card ? 
Options: a ) 2 / 15 , b ) 2 / 13 , c ) 1 / 15 , d ) 4 / 13 , e ) 5 / 7
Output: d
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 ? 
Options: a ) 20 / 969 , b ) 20 / 875 , c ) 21 / 876 , d ) 3 / 512 , e ) 2 / 9
Output: a
Problem: the letters o , l and t are rearranged to form the word ' lot ' . find its probability . 
Options: a ) 1 / 18 , b ) 1 / 12 , c ) 1 / 4 , d ) 1 / 8 , e ) 1 / 6
Output: e
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 ? 
Options: a ) 12 / 13 , b ) 11 / 13 , c ) 10 / 15 , d ) 1 / 15 , e ) 4 / 14
Output: b
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 ? 
Options: a ) 25 / 323 , b ) 21 / 969 , c ) 28 / 989 , d ) 74 / 879 , e ) 23 / 589
Output: a
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 . 
Options: a ) 1 / 6 , b ) 4 / 120 , c ) 29 / 30 , d ) 1 / 9 , e ) none of these
Output: c
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 ? 
Options: a ) 18 / 35 , b ) 16 / 35 , c ) 14 / 35 , d ) 13 / 35 , e ) 12 / 35
Output: a
Problem: a , b , c , d , e , f , g , h sitting in a row what is the probability that a , b , c sitting together ? 
Options: a ) 3 / 14 , b ) 5 / 28 , c ) 3 / 28 , d ) 1 / 7 , e ) 9 / 28
Output: c
Problem: a , b , c , d , e , f , g , h sitting in a row what is the probability that a , b , d are sitting together ? 
Options: a ) 1 / 5 , b ) 3 / 28 , c ) 1 / 7 , d ) 1 / 14 , e ) 5 / 28
Output: b
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 
Options: a ) 1 / 8 , b ) 1 / 6 , c ) 1 / 4 , d ) 3 / 4 , e ) 7 / 8
Output: a
Problem: in a throw of dice what is the probability of ge æ « ng number greater than 4 
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 5 , d ) 1 / 6 , e ) none of these
Output: b
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 ? 
Options: a ) 110 , b ) 146 , c ) 152 , d ) 162 , e ) 170
Output: a
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 ? 
Options: a ) 1 / 35 , b ) 1 / 9 , c ) 1 / 10 , d ) 1 / 20 , e ) 1 / 30
Output: a
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 ? 
Options: a ) 55 % , b ) 60 % , c ) 70 % , d ) 72 % , e ) 95 %
Output: e
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 - . 
Options: a ) 216 , b ) 243 , c ) 215 , d ) 729 , e ) 728
Output: c
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 ? 
Options: a ) 17 / 30 , b ) 2 / 5 , c ) 7 / 15 , d ) 4 / 15 , e ) 11 / 30
Output: e
Problem: find the probability that a leap year chosen at random will have 53 sundays 
Options: a ) 2 / 7 , b ) 2 / 6 , c ) 2 / 5 , d ) 2 / 3 , e ) 2 / 4
Output: a
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 ? 
Options: a ) 15 / 56 , b ) 41 / 56 , c ) 13 / 28 , d ) 15 / 28 , e ) 5 / 14
Output: d
Problem: from a pack of 52 cards , 1 card is drawn at random . find the probability of a face card drawn 
Options: a ) 4 / 13 , b ) 1 / 52 , c ) 1 / 4 , d ) 1 / 5 , e ) none of above
Output: a
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 ? 
Options: a ) 3 / 5 , b ) 1 / 2 , c ) 3 / 4 , d ) 3 / 8 , e ) 3 / 6
Output: d
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 ? 
Options: a ) 4586 , b ) 5896 , c ) 2415 , d ) 1771 , e ) 1881
Output: d
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 ? 
Options: a ) 1 / 4 , b ) 1 / 2 , c ) 1 / 2 , d ) 5 / 8 , e ) 2
Output: e
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 ? 
Options: a ) 0.12 , b ) 0.23 , c ) 0.35 , d ) 0.45 , e ) 0.65
Output: b
Problem: in how many ways can 5 people be arranged in a circle ? 
Options: a ) 2 ! , b ) 5 ! , c ) 4 ! , d ) 3 ! , e ) 6 !
Output: c
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 ? 
Options: a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 5 / 22
Output: d
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 ? 
Options: a ) 1 / 8 , b ) 1 / 4 , c ) 1 / 2 , d ) 3 / 4 , e ) 7 / 8
Output: d
Problem: six 6 faced dice are thrown together . the probability that all the three show the same number on them is ? 
Options: a ) 1 / 32 , b ) 1 / 7776 , c ) 1 / 33 , d ) 1 / 38 , e ) 1 / 34
Output: b
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 
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Output: c
Problem: there are 7 girls and 3 chairs . in how many ways girls can occupy the chairs ? 
Options: a ) 760 , b ) 210 , c ) 560 , d ) 740 , e ) 800
Output: b
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 : 
Options: a ) 2 / 109 , b ) 7 / 109 , c ) 8 / 223 , d ) 14 / 263 , e ) 13 / 102
Output: e
Problem: what is the probability of getting only 1 head in a single throw of four fair coins ? 
Options: a ) 1 / 2 , b ) 3 / 8 , c ) 1 / 4 , d ) 1 / 5 , e ) 5 / 8
Output: c
Problem: what is the smallest number by which 2880 must be divided in order to make it into a perfect square ? 
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Output: c
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 ? 
Options: a ) 1 / 12 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 2 , e ) 1 / 6
Output: a
Problem: what is the probability of getting exactly 2 heads in a single throw of five fair coins ? 
Options: a ) 1 / 4 , b ) 3 / 8 , c ) 3 / 16 , d ) 5 / 16 , e ) 11 / 32
Output: d
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 . 
Options: a ) 20 , b ) 120 , c ) 210 , d ) 15 , e ) 45
Output: b
Problem: a coin is tossed 7 times . what is the probability of getting exactly 6 heads ? 
Options: a ) 7 / 32 , b ) 3 / 64 , c ) 5 / 64 , d ) 3 / 128 , e ) 7 / 128
Output: e
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 ? 
Options: a ) 3 / 5 , b ) 4 / 5 , c ) 17 / 25 , d ) 21 / 25 , e ) 43 / 50
Output: d
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 ? 
Options: a ) 3 / 40,000 , b ) 1 / 3,600 , c ) 1 / 20,000 , d ) 1 / 60 , e ) 1 / 15
Output: c
Problem: 8 coins are tossed . whats is the probability that one and only one turns up head ? 
Options: a ) 1 / 256 , b ) 1 / 32 , c ) 1 / 64 , d ) 1 / 128 , e ) 1 / 189
Output: b
Problem: how many positive integers less than 600 can be formed using the numbers 1 , 2 , 3 and 5 for the digits ? 
Options: a ) 48 , b ) 52 , c ) 66 , d ) 68 , e ) 84
Output: e
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 ? 
Options: a ) 2 / 3 , b ) 5 / 8 , c ) 3 / 5 , d ) 3 / 8 , e ) 4 / 9
Output: b
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 ? 
Options: a ) 0 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 1
Output: d
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 ? 
Options: a ) 17 / 30 , b ) 2 / 5 , c ) 3 / 10 , d ) 4 / 15 , e ) 11 / 30
Output: c
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 ? 
Options: a ) 100 , b ) 105 , c ) 115 , d ) 120 , e ) 125
Output: c
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 . 
Options: a ) a . 240 , b ) b . 808250 , c ) c . 502450 , d ) d . 784200 , e ) e . 302400
Output: a
Problem: in a throw of dice what is the probability of ge æ « ng number greater than 3 
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 5 , d ) 1 / 6 , e ) none of these
Output: a
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 : 
Options: a ) 1 / 13 , b ) 1 / 26 , c ) 2 / 13 , d ) 1 / 52 , e ) 1 / 48
Output: b
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 ? 
Options: a ) 3 / 4 , b ) 2 / 4 , c ) 1 / 4 , d ) 1 / 8 , e ) 1 / 16
Output: a
Problem: in how many ways 4 boys and 3 girls can be seated in a row so that they are alternative ? 
Options: a ) 120 , b ) 144 , c ) 160 , d ) 210 , e ) 180
Output: b
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 ? 
Options: a ) 3 / 4 , b ) 5 / 8 , c ) 7 / 8 , d ) 9 / 16 , e ) 15 / 16
Output: c
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 ? 
Options: a ) 2 / 3 , b ) 6 / 7 , c ) 5 / 7 , d ) 8 / 7 , e ) 4 / 3
Output: c
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 ? 
Options: a ) 1 / 7 , b ) 1 / 8 , c ) 1 / 9 , d ) 1 / 10 , e ) 1 / 25
Output: a
Problem: a fair coin is tossed 4 times . what is the probability of getting at least 2 tails ? 
Options: a ) 1 / 16 , b ) 1 / 2 , c ) 3 / 16 , d ) 11 / 16 , e ) 3 / 8
Output: d
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 ? 
Options: a ) 1 / 3 , b ) 4 / 9 , c ) 5 / 6 , d ) 3 / 7 , e ) 1 / 4
Output: c
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 . 
Options: a ) 0.3995 , b ) 0.4995 , c ) 0.5995 , d ) 0.6995 , e ) 0.7995
Output: b
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 ? 
Options: a ) 10 / 30 , b ) 1 / 30 , c ) 8 / 30 , d ) 3 / 30 , e ) 7 / 30
Output: c