niryuu/sni-each-converted huggingface dataset:
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 ? 
Options: a ) 2 / 7 , b ) 5 / 7 , c ) 4 / 7 , d ) 3 / 15 , e ) 3 / 14
Output: e
Problem: if two dice are thrown together , the probability of getting a doublet on the dice is 
Options: a ) 1 / 6 , b ) 1 / 5 , c ) 1 / 4 , d ) 1 / 3 , e ) 1 / 2
Output: a
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 ? 
Options: a ) 0.06 , b ) ( 0.06 ) ^ 25 , c ) 1 - ( 0.06 ) ^ 25 , d ) 1 - ( 0.94 ) ^ 25 , e ) ( 0.94 ) ^ 25
Output: d
Problem: the probability that a number selected at random from the first 50 natural numbers is a composite number is - . 
Options: a ) 17 / 25 , b ) 17 / 27 , c ) 17 / 18 , d ) 17 / 22 , e ) 17 / 09
Output: a
Problem: what is the probability of getting exactly 2 heads in a single throw of four fair coins ? 
Options: a ) 1 / 2 , b ) 3 / 4 , c ) 3 / 8 , d ) 3 / 16 , e ) 5 / 16
Output: c
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 ? 
Options: a ) 140 , b ) 146 , c ) 152 , d ) 162 , e ) 183
Output: e
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 ? 
Options: a ) 1 / 4 , b ) 1 / 5 , c ) 1 / 6 , d ) 1 / 9 , e ) 1 / 12
Output: c
Problem: two unbiased coins are tossed . what is probability of getting at most one tail ? 
Options: a ) 12 , b ) 13 , c ) 32 , d ) 34 , e ) none of these
Output: d
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 ? 
Options: a ) 1 / 16 , b ) 2 / 14 , c ) 1 / 12 , d ) 1 / 19 , e ) 1 / 17
Output: c
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 ? 
Options: a ) 2 / 7 , b ) 3 / 5 , c ) 3 / 11 , d ) 18 / 85 , e ) 7 / 16
Output: d
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 ? 
Options: a ) 1 / 2 , b ) 1 / 5 , c ) 3 / 4 , d ) 1 / 3 , e ) 3 / 5
Output: a
Problem: in how many ways 3 boys and 3 girls can be seated in a row so that they are alternate . 
Options: a ) 144 , b ) 288 , c ) 36 , d ) 256 , e ) none
Output: c
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 ? 
Options: a ) 1 / 6 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 6
Output: c
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 ? 
Options: a ) 1 / 4 , b ) 1 / 6 , c ) 1 / 8 , d ) 1 / 12 , e ) 1 / 16
Output: c
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 ? 
Options: a ) 1 / 35 , b ) 1 / 10 , c ) 1 / 3 , d ) 1 / 4 , e ) 1 / 5
Output: c
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 ? 
Options: a ) 9 / 100 , b ) 2 / 19 , c ) 1 / 8 , d ) 3 / 20 , e ) 3 / 10
Output: b
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 . 
Options: a ) 1.35 , b ) 2.91 , c ) 3.12 , d ) 4.36 , e ) 5.15
Output: d
Problem: what is the probability of getting a queen or spade from a set of cards ? 
Options: a ) 3 / 13 , b ) 4 / 13 , c ) 5 / 13 , d ) 6 / 13 , e ) 7 / 13
Output: b
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 ? 
Options: a ) 1 / 6 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 6
Output: d
Problem: in a throw of dice what is the probability of ge æ « ng number greater than 1 
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 5 , d ) 5 / 6 , e ) none of these
Output: e
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 ? 
Options: a ) 3 / 4 , b ) 2 / 4 , c ) 1 / 4 , d ) 1 / 8 , e ) 9 / 10
Output: e
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 . 
Options: a ) 4 / 9 , b ) 6 / 11 , c ) 8 / 15 , d ) 10 / 21 , e ) 12 / 25
Output: d
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 ? 
Options: a ) 1 / 6 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 6
Output: a
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 ? 
Options: a ) 55 % , b ) 60 % , c ) 70 % , d ) 72 % , e ) 80 %
Output: e
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 ? 
Options: a ) 9 / 100 , b ) 2 / 19 , c ) 1 / 8 , d ) 3 / 20 , e ) 3 / 10
Output: e
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 
Options: a ) 1 / 7 , b ) 1 / 8 , c ) 1 / 4 , d ) 3 / 4 , e ) 4 / 9
Output: e
Problem: a card is drawn from a pack of 52 cards the probability of getting queen of club or aking of a heart ? 
Options: a ) 8 / 58 , b ) 9 / 25 , c ) 1 / 26 , d ) 6 / 25 , e ) 8 / 45
Output: c
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 ? 
Options: a ) 4 / 9 , b ) 5 / 9 , c ) 17 / 27 , d ) 23 / 27 , e ) 65 / 81
Output: e
Problem: three coins are tossed . find the probability of at most 2 tails ? 
Options: a ) 1 / 2 , b ) 1 / 4 , c ) 2 / 3 , d ) 7 / 8 , e ) 3 / 8
Output: d
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 ? 
Options: a ) 67 , b ) 73 , c ) 79 , d ) 85 , e ) 91
Output: e
Problem: a fair coin is tossed 9 times . what is the probability of getting more heads than tails in 9 tosses ? 
Options: a ) 1 / 2 , b ) 63 / 128 , c ) 4 / 7 , d ) 61 / 256 , e ) 63 / 64
Output: a
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 ? 
Options: a ) 12 / 29 , b ) 14 / 31 , c ) 16 / 33 , d ) 18 / 35 , e ) 20 / 37
Output: d
Problem: there are 4 red shoes & 6 green shoes . if two of red shoes are drawn what is the probability of getting red shoes 
Options: a ) 1 / 13 , b ) 1 / 14 , c ) 1 / 2 , d ) 2 / 15 , e ) 2 / 16
Output: d
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 ? 
Options: a ) 1540 , b ) 2314 , c ) 5420 , d ) 1240 , e ) 4512
Output: a
Problem: from a pack of 52 cards , 1 card is drawn at random . what is the probability that a heart is drawn ? 
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 13 , e ) 3 / 26
Output: c
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 ? 
Options: a ) a ) 40 , b ) b ) 45 , c ) c ) 50 , d ) d ) 55 , e ) e ) 111
Output: e
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 ? 
Options: a ) 1 / 3 , b ) 5 / 9 , c ) 7 / 9 , d ) 19 / 27 , e ) 23 / 27
Output: d
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 . 
Options: a ) 53 , b ) 54 , c ) 55 , d ) 56 , e ) 57
Output: d
Problem: how many positive integers less than 400 can be formed using the numbers 1 , 2 , 3 and 5 for the digits ? 
Options: a ) 48 , b ) 52 , c ) 66 , d ) 84 , e ) 68
Output: e
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 ? 
Options: a ) 1 / 6 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 6
Output: e
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 ? 
Options: a ) 1 / 2 , b ) 5 / 400 , c ) 1 / 5 , d ) 1 / 3 , e ) 1 / 4
Output: e
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 ? 
Options: a ) 1 / 8 , b ) 1 / 32 , c ) 1 / 4 , d ) 1 / 2 , e ) 1 / 16
Output: b
Problem: three unbiased coins are tossed . what is the probability of getting 3 heads ? 
Options: a ) 3 / 4 , b ) 1 / 4 , c ) 3 / 8 , d ) 7 / 8 , e ) 1 / 8
Output: e
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 ? 
Options: a ) 9 / 100 , b ) 2 / 19 , c ) 1 / 8 , d ) 3 / 20 , e ) 3 / 10
Output: b
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 ? 
Options: a ) 50 , b ) 42 , c ) 24 , d ) 20 , e ) 12
Output: b
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 ) 8 / 13 , b ) 6 / 13 , c ) 3 / 13 , d ) 4 / 13 , e ) 1 / 13
Output: d
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 ? 
Options: a ) a ) 30 , b ) b ) 45 , c ) c ) 50 , d ) d ) 55 , e ) e ) 60
Output: a
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 ? 
Options: a ) 65 , b ) 87 , c ) 71 , d ) 60 , e ) 66
Output: c
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 
Options: a ) 7 / 19 , b ) 6 / 19 , c ) 5 / 19 , d ) 4 / 19 , e ) none of these
Output: a
Problem: find the probability that a leap year selected at random will not have 53 sundays 
Options: a ) 6 / 7 , b ) 5 / 7 , c ) 4 / 7 , d ) 3 / 7 , e ) 2 / 7
Output: b
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 ? 
Options: a ) 1 / 9 , b ) 1 / 2 , c ) 1 / 1 , d ) 1 / 5 , e ) 1 / 8
Output: b
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 ? 
Options: a ) 3 / 4 , b ) 5 / 11 , c ) 1 / 7 , d ) 1 / 8 , e ) 4 / 3
Output: b
Problem: three 6 faced dice are thrown together . the probability that exactly two dice show the same number on them is 
Options: a ) 5 / 15 , b ) 5 / 12 , c ) 5 / 19 , d ) 5 / 12 , e ) 5 / 11
Output: b
Problem: rhoda tosses a coin 5 times . find the probability of getting exactly 4 heads . 
Options: a ) 5 / 32 , b ) 6 / 32 , c ) 5 / 16 , d ) 4 / 32 , e ) 8 / 32
Output: a
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 ? 
Options: a ) 2 / 13 , b ) 3 / 13 , c ) 1 / 26 , d ) 1 / 52 , e ) 3 / 52
Output: c
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 ? 
Options: a ) 7 / 4 , b ) 1 / 2 , c ) 1 / 2 , d ) 5 / 8 , e ) 2 / 3
Output: a
Problem: the probability that a number selected at random from first 50 natural numbers is a composite number is 
Options: a ) 21 / 25 , b ) 17 / 25 , c ) 4 / 25 , d ) 8 / 25 , e ) 10 / 25
Output: b
Problem: in a throw of dice what is the probability of getting number greater than 5 
Options: a ) 1 / 7 , b ) 1 / 6 , c ) 1 / 11 , d ) 1 / 13 , e ) 2 / 9
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 3 flips but not on the last 3 flips ? 
Options: a ) 1 / 8 , b ) 1 / 16 , c ) 1 / 32 , d ) 1 / 64 , e ) 1 / 128
Output: d
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 ? 
Options: a ) 1 / 10 , b ) 4 / 9 , c ) 1 / 2 , d ) 3 / 5 , e ) 2 / 3
Output: d
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 ? 
Options: a ) 2 / 3 , b ) 5 / 8 , c ) 3 / 5 , d ) 4 / 7 , e ) 5 / 8
Output: b
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 ? 
Options: a ) 4 / 15 , b ) 3 / 40 , c ) 13 / 40 , d ) 7 / 20 , e ) 13 / 22
Output: a
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 ? 
Options: a ) 3 / 40000 , b ) 1 / 3600 , c ) 9 / 2000 , d ) 1 / 60 , e ) 1 / 15
Output: a
Problem: in how many ways 2 boys and 2 girls can be seated in a row so that boys and girls are alternate ? 
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Output: b
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 ? 
Options: a ) 12 % , b ) 20 % , c ) 33 % , d ) 40 % , e ) 50 %
Output: d
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 ? 
Options: a ) 1 / 35 , b ) 1 / 10 , c ) 1 / 15 , d ) 1 / 20 , e ) 1 / 25
Output: b
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 ? 
Options: a ) 1 / 8 , b ) 1 / 4 , c ) 1 / 3 , d ) 3 / 8 , e ) 1 / 2
Output: b
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 ? 
Options: a ) 1 / 5 , b ) 2 / 7 , c ) 2 / 9 , d ) 3 / 5 , e ) 4 / 11
Output: b
Problem: from a pack of 52 cards , 1 card is drawn at random . what is the probability that a red king is drawn ? 
Options: a ) 1 / 2 , b ) 1 / 4 , c ) 1 / 13 , d ) 1 / 26 , e ) 1 / 52
Output: d
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 ? 
Options: a ) 1 / 200 , b ) 1 / 100 , c ) 90 / 2900 , d ) 17 / 2700 , e ) 1 / 20
Output: d
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 ? 
Options: a ) 1 / 4 , b ) 1 / 8 , c ) 1 / 2 , d ) 1 / 16 , e ) 1 / 32
Output: d
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 ? 
Options: a ) 1 / 2 , b ) 3 / 4 , c ) 2 / 3 , d ) 1 / 5 , e ) 3 / 7
Output: c
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 ? 
Options: a ) 12 / 55 , b ) 3 / 5 , c ) 3 / 11 , d ) 1 / 4 , e ) 7 / 16
Output: a
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 ? 
Options: a ) 110 , b ) 70 , c ) 120 , d ) 130 , e ) 140
Output: b
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 ? 
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
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 blue balls ? 
Options: a ) 1 / 18 , b ) 1 / 24 , c ) 1 / 30 , d ) 1 / 36 , e ) 1 / 48
Output: c
Problem: when you draw 2 dices together , find the probability of getting a total of 6 ? 
Options: a ) 3 / 13 , b ) 2 / 31 , c ) 5 / 36 , d ) 7 / 41 , e ) 7 / 43
Output: c
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 ? 
Options: a ) 12 . , b ) 9 . , c ) 8 . , d ) 7 . , e ) 6 .
Output: a
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 ? 
Options: a ) 2 / 7 , b ) 3 / 5 , c ) 3 / 13 , d ) 1 / 4 , e ) 7 / 16
Output: c
Problem: 4 dice are thrown simultaneously on the board . find the probability show the same face . 
Options: a ) 1 / 213 , b ) 1 / 215 , c ) 1 / 216 , d ) 2 / 113 , e ) 3 / 114
Output: c
Problem: what is the probability that a two digit number selected at random is a multiple of 3 and not a multiple of 5 ? 
Options: a ) 1 / 15 , b ) 2 / 15 , c ) 4 / 15 , d ) 7 / 15 , e ) none of these
Output: c
Problem: in a throw of a coin probability of getting a head . 
Options: a ) 1 / 3 , b ) 2 / 3 , c ) 1 / 4 , d ) 2 / 5 , e ) 1 / 2
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 j 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: 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 ? 
Options: a ) 10 hr , b ) 5 hr , c ) 6 hr , d ) 4 hr 30 min , e ) 5 hr 12 min
Output: e
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 ? 
Options: a ) 1 / 33 , b ) 2 / 63 , c ) 1 / 3 , d ) 43 / 62 , e ) 11 / 12
Output: d
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 ? . 
Options: a ) 12 / 91 , b ) 3 / 15 , c ) 12 / 15 , d ) 33 / 91 , e ) 3 / 91
Output: d
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 ? 
Options: a ) 2 / 5 , b ) 1 / 5 , c ) 1 / 9 , d ) 1 / 10 , e ) 1 / 15
Output: e
Problem: two coins are tossed . find the probability of at most 2 tails ? 
Options: a ) 1 / 2 , b ) 1 / 4 , c ) 1 / 3 , d ) 1 , e ) 3 / 4
Output: d
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 ? 
Options: a ) 20 / 323 , b ) 40 / 323 , c ) 60 / 273 , d ) 50 / 373 , e ) 40 / 373
Output: b
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 ? 
Options: a ) 1 / 5 , b ) 3 / 20 , c ) 2 / 15 , d ) 1 / 12 , e ) 1 / 10
Output: d
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 ? 
Options: a ) 1 / 6 , b ) 1 / 8 , c ) 1 / 12 , d ) 1 / 16 , e ) 1 / 32
Output: d
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 ? 
Options: a ) 1 / 13 , b ) 1 / 15 , c ) 1 / 26 , d ) 1 / 52 , e ) 1 / 104
Output: e
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 . 
Options: a ) 1 / 144 , b ) 1 / 25 , c ) 1 / 12 , d ) 1 / 6 , e ) 1 / 3
Output: b
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 / 3 , e ) none of these
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 / 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 ? 
Options: a ) 134 , b ) 146 , c ) 152 , d ) 162 , e ) 170
Output: a
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 ? 
Options: a ) 60 , b ) 80 , c ) 100 , d ) 120 , e ) 140
Output: d
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 ? 
Options: a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 5 / 22
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 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 ? 
Options: a ) 1 / 20 , b ) 3 / 40 , c ) 13 / 40 , d ) 7 / 20 , e ) 13 / 22
Output: a
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 ? 
Options: a ) 75 , b ) 120 , c ) 210 , d ) 246 , e ) 252
Output: d
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 ? 
Options: a ) 2 / 7 , b ) 3 / 5 , c ) 3 / 11 , d ) 1 / 4 , e ) 7 / 16
Output: a
Problem: find the probability that the number drawn is a multiple of 6 and 8 . 
Options: a ) 3 / 50 , b ) 2 / 25 , c ) 1 / 50 , d ) 1 / 25 , e ) 4 / 25
Output: d
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 ? 
Options: a ) 30 , b ) 45 , c ) 55 , d ) 65 , e ) 70
Output: a
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 ? 
Options: a ) a ) 40 , b ) b ) 45 , c ) c ) 36 , d ) d ) 55 , e ) e ) 60
Output: c
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 ? 
Options: a ) 2 / 3 , b ) 5 / 8 , c ) 5 / 4 , d ) 5 / 6 , e ) 6 / 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 w 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: what is the probability of getting 53 mondays in a leap year ? 
Options: a ) 1 / 7 , b ) 2 / 7 , c ) 3 / 7 , d ) 4 / 7 , e ) 5 / 7
Output: b
Problem: what is the probability that company g ' s advertisement will be one of the first two be shown during the first commercial break ? 
Options: a ) 1 / 225 , b ) 1 / 30 , c ) 1 / 15 , d ) 2 / 15 , e ) 4 / 15
Output: d
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 ? 
Options: a ) 22 , b ) 87 , c ) 29 , d ) 26 , e ) 191
Output: b
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 ? 
Options: a ) 120 , b ) 110 , c ) 105 , d ) 140 , e ) 135
Output: d
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 . 
Options: a ) 2 / 11 , b ) 4 / 15 , c ) 6 / 17 , d ) 8 / 21 , e ) 10 / 25
Output: d
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 ? 
Options: a ) 1 / 5 , b ) 3 / 20 , c ) 1 / 8 , d ) 3 / 10 , e ) 1 / 10
Output: c
Problem: a coin is tossed 8 times . what is the probability of getting exactly 7 heads ? 
Options: a ) 1 / 8 , b ) 1 / 16 , c ) 1 / 32 , d ) 1 / 64 , e ) 1 / 128
Output: c
Problem: how many positive integers less than 500 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: d
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 ? 
Options: a ) 0.1 , b ) 0.001 , c ) 0.0002 , d ) 1.0 e - 05 , e ) 0.0001
Output: d
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 - . 
Options: a ) 1 / 3 , b ) 1 / 2 , c ) 7 / 8 , d ) 3 / 4 , e ) 7 / 3
Output: b
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 ? 
Options: a ) 3 / 40,000 , b ) 1 / 3,600 , c ) 9 / 2,000 , d ) 1 / 60 , e ) 1 / 16,000
Output: e
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 
Options: a ) 4 / 19 , b ) 7 / 19 , c ) 12 / 19 , d ) 21 / 99 , e ) 26 / 77
Output: e
Problem: a fair coin is tossed 3 times . what is the probability of getting at least 2 heads ? 
Options: a ) 3 / 4 , b ) 3 / 2 , c ) 1 / 4 , d ) 1 / 2 , e ) 1 / 5
Output: d
Problem: a coin is tossed 3 times . what is the probability of getting exactly 2 heads ? 
Options: a ) 1 / 2 , b ) 1 / 4 , c ) 3 / 8 , d ) 5 / 8 , e ) 3 / 16
Output: c
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 ? 
Options: a ) 70 / 323 , b ) 50 / 323 , c ) 52 / 969 , d ) 60 / 323 , e ) 25 / 321
Output: a
Problem: how many cubes of 3 cm edge can be cut out of a cube of 18 cm edge 
Options: a ) 36 , b ) 232 , c ) 216 , d ) 455 , e ) 363
Output: c
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 ? 
Options: a ) 12 % , b ) 20 % , c ) 33 % , d ) 40 % , e ) 50 %
Output: d
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 ? 
Options: a ) 3 / 4 , b ) 7 / 8 , c ) 15 / 16 , d ) 31 / 32 , e ) 63 / 64
Output: e
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: 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 ? 
Options: a ) 7 / 13 , b ) 15 / 26 , c ) 9 / 12 , d ) 8 / 13 , e ) 29 / 52
Output: d
Problem: how many cubes of 2 cm edge can be cut out of a cube of 24 cm edge 
Options: a ) 1136 , b ) 1728 , c ) 1216 , d ) 1484 , e ) none of these
Output: b
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 ? 
Options: a ) 15 / 64 , b ) 30 / 64 , c ) 1 / 2 , d ) 1 / 4 , e ) 52 / 64
Output: a
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 ? 
Options: a ) 25 / 28 , b ) 27 / 28 , c ) 30 / 28 , d ) 40 / 28 , e ) 50 / 28
Output: b
Problem: in how many ways 4 boys and 4 girls can be seated in a row so that boys and girls are alternate ? 
Options: a ) 1152 , b ) 1987 , c ) 2012 , d ) 1856 , e ) 2546
Output: a
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 ? 
Options: a ) 4 , b ) 4 / 3 , c ) 4 / 5 , d ) 4 / 9 , e ) 3 / 5
Output: e
Problem: in how many ways 6 boys and 4 girls can be seated in a row so that they are alternative ? 
Options: a ) 14420 , b ) 12620 , c ) 17280 , d ) 21200 , e ) 24560
Output: c
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 ? 
Options: a ) 2 / 27 , b ) 1 / 9 , c ) 1 / 3 , d ) 4 / 27 , e ) 2 / 9
Output: d
Problem: when two dice are tossed , what is the probability that the total score is a prime number ? 
Options: a ) 1 / 6 , b ) 3 , c ) 5 / 12 , d ) 7 / 12 , e ) 9 / 12
Output: c
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 ? 
Options: a ) 12 . , b ) 9 . , c ) 8 . , d ) 7 . , e ) 6 .
Output: d
Problem: in how many ways 3 boys and 3 girls can be seated in a row so that boys and girls are alternate ? 
Options: a ) 69 , b ) 70 , c ) 71 , d ) 72 , e ) 73
Output: d
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 . 
Options: a ) 36 , b ) 40 , c ) 45 , d ) 51 , e ) 56
Output: a
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 
Options: a ) 3 / 10 , b ) 7 / 19 , c ) 12 / 19 , d ) 21 / 95 , e ) none
Output: a
Problem: what is the probability of getting exactly three heads on five flips of a fair coin ? 
Options: a ) 1 / 32 , b ) 3 / 32 , c ) 1 / 4 , d ) 5 / 16 , e ) 1 / 2
Output: d
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 . 
Options: a ) 1 / 144 , b ) 1 / 36 , c ) 1 / 12 , d ) 1 / 6 , e ) 1 / 49
Output: e
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 ? 
Options: a ) 1 / 6 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 6
Output: b
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 ? 
Options: a ) 2 / 3 , b ) 5 / 8 , c ) 5 / 9 , d ) 3 / 7 , e ) 4 / 7
Output: b
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 ? 
Options: a ) 0.02 , b ) ( 0.02 ) ^ 13 , c ) 1 - ( 0.02 ) ^ 13 , d ) ( 0.98 ) ^ 13 , e ) 1 - ( 0.98 ) ^ 13
Output: e
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 ? 
Options: a ) 1 / 7 , b ) 2 / 4 , c ) 3 / 4 , d ) 1 / 8 , e ) 1 / 16
Output: c
Problem: what is the probability of randomly selecting one of the shortest diagonals from all the diagonals of a regular 11 - sided polygon ) ? 
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 8 , e ) 1 / 11
Output: c
Problem: there are 21 students in a class . in how many different ways can a committee of 3 students be formed ? 
Options: a ) 1180 , b ) 1330 , c ) 1540 , d ) 1760 , e ) 1920
Output: b
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 . 
Options: a ) 40 , b ) 49 , c ) 41 , d ) 56 , e ) 42
Output: e
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 ? 
Options: a ) 1 / 5 , b ) 2 / 7 , c ) 2 / 5 , d ) 1 / 7 , e ) 3 / 5
Output: b
Problem: when fair coin is tossed 9 times find the probability of getting head at least once . 
Options: a ) 1 / 512 , b ) 511 / 512 , c ) 9 / 512 , d ) 503 / 51 , e ) 503 / 510
Output: b
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 ? 
Options: a ) 2 , b ) 3 , c ) 30 , d ) 6 , e ) 12
Output: c
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 ? 
Options: a ) 20 , b ) 25 , c ) 30 , d ) 35 , e ) 40
Output: b
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 
Options: a ) 4 / 19 , b ) 7 / 19 , c ) 12 / 37 , d ) 21 / 95 , e ) none
Output: c
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 } 
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Output: e
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 ? 
Options: a ) 1 / 720 , b ) 1 / 80 , c ) 1 / 10 , d ) 1 / 9 , e ) 1 / 5
Output: e
Problem: what is the probability of randomly selecting one of the shortest diagonals from all the diagonals of a regular decagon ( 10 - sided polygon ) ? 
Options: a ) 3 / 10 , b ) 2 / 5 , c ) 2 / 7 , d ) 10 / 21 , e ) 5 / 11
Output: c
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 ? 
Options: a ) . 5 , b ) 0.6 , c ) 0.4 , d ) 0.7 , e ) 0.8
Output: e
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 ? 
Options: a ) 9 / 100 , b ) 2 / 19 , c ) 1 / 8 , d ) 3 / 20 , e ) 3 / 10
Output: e
Problem: in how many ways 7 boys and 7 girls can be seated in a row so that boys and girls are alternate ? 
Options: a ) 50803200 , b ) 50328000 , c ) 50003280 , d ) 50703200 , e ) 50603200
Output: a
Problem: what is the probability of getting exactly 1 head in a single throw of five fair coins ? 
Options: a ) 1 / 4 , b ) 3 / 8 , c ) 3 / 16 , d ) 5 / 32 , e ) 7 / 32
Output: d
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 ? 
Options: a ) 1 / 26 , b ) 1 / 13 , c ) 3 / 52 , d ) 3 / 26 , e ) 15 / 26
Output: a
Problem: what is the probability of randomly selecting one of the shortest diagonals from all the diagonals of a regular 7 - sided polygon ) ? 
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 6 , e ) 1 / 7
Output: a
Problem: two unbiased coins are tossed . find the probability of getting two heads ? 
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 2 / 3 , e ) 3 / 5
Output: c
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 
Options: a ) 8 / 2652 , b ) 18 / 2652 , c ) 1 / 2652 , d ) 12 / 2652 , e ) 16 / 2652
Output: b
Problem: four 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 / 216 , c ) 1 / 33 , d ) 1 / 38 , e ) 1 / 34
Output: b
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 ? 
Options: a ) a ) 40 , b ) b ) 14 , c ) c ) 50 , d ) d ) 55 , e ) e ) 60
Output: b
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 ? 
Options: a ) 42 % , b ) 48 % , c ) 54 % , d ) 60 % , e ) 66 %
Output: c
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 ? 
Options: a ) 2 / 7 , b ) 3 / 5 , c ) 3 / 11 , d ) 1 / 4 , e ) 7 / 16
Output: d
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 . 
Options: a ) 2 / 7 , b ) 3 / 11 , c ) 4 / 15 , d ) 5 / 21 , e ) 6 / 25
Output: d
Problem: how many cubes of 8 cm edge can be cut out of a cube of 16 cm edge 
Options: a ) 36 , b ) 2 , c ) 8 , d ) 48 , e ) none of these
Output: c
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 ? 
Options: a ) 12 , b ) 9 , c ) 8 , d ) 7 , e ) 6
Output: e
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 ? 
Options: a ) 100 , b ) 200 , c ) 350 , d ) 150 , e ) 140
Output: d
Problem: what is the probability of getting atmost one head when two unbiased coin are tossed ? 
Options: a ) 3 / 4 , b ) 3 / 2 , c ) 4 / 3 , d ) 1 / 2 , e ) 2 / 6
Output: a
Problem: three unbiased coins are tossed , what is the probability of ge ƫ ng at least 2 tails ? 
Options: a ) 1 / 3 , b ) 1 / 6 , c ) 1 / 2 , d ) 1 / 8 , e ) none of these
Output: c
Problem: three coins are tossed . find the probability of at least 1 head and 1 tail ? 
Options: a ) 1 / 2 , b ) 1 / 4 , c ) 3 / 4 , d ) 7 / 8 , e ) 1 / 8
Output: c
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 ? 
Options: a ) 1 / 8 , b ) 1 / 4 , c ) 1 / 16 , d ) 1 / 2 , e ) 1 / 32
Output: a
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 ? 
Options: a ) 9 / 100 , b ) 2 / 19 , c ) 1 / 8 , d ) 1 / 20 , e ) 3 / 10
Output: d
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 ? 
Options: a ) 1 / 7 , b ) 1 / 9 , c ) 2 / 7 , d ) 3 / 7 , e ) 2 / 9
Output: b
Problem: two dice are thrown simultaneously . what is the probability of getting two numbers whose product is not an even ? 
Options: a ) 1 / 2 , b ) 1 / 4 , c ) 2 / 3 , d ) 2 / 5 , e ) 3 / 7
Output: b
Problem: find the probability that a non leap year selected at random will have 53 sundays 
Options: a ) 6 / 7 , b ) 5 / 7 , c ) 4 / 7 , d ) 3 / 7 , e ) 1 / 7
Output: e
Problem: from a pack of 52 cards , 1 card is drawn at random . what is the probability that a red card is drawn ? 
Options: a ) 1 / 2 , b ) 1 / 4 , c ) 1 / 26 , d ) 1 / 13 , e ) 5 / 13
Output: a
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 ? 
Options: a ) 1100 , b ) 1200 , c ) 1235 , d ) 1354 , e ) 735
Output: e
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 ? 
Options: a ) 18 , b ) 20 , c ) 16 , d ) 22 , e ) 24
Output: c
Problem: in a single throw of a die , what is probability of getting a number greater than 4 ? 
Options: a ) 2 / 3 , b ) 3 / 5 , c ) 4 / 7 , d ) 8 / 9 , e ) 1 / 3
Output: e
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 ? 
Options: a ) 950 , b ) 1050 , c ) 2150 , d ) 2050 , e ) 1000
Output: b
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 ? 
Options: a ) 3 / 20,000 , b ) 1 / 3,600 , c ) 9 / 2,000 , d ) 1 / 60 , e ) 1 / 15
Output: a
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 
Options: a ) 1 / 7 , b ) 1 / 8 , c ) 2 / 5 , d ) 3 / 4 , e ) 7 / 8
Output: c
Problem: a coin is tossed 4 times . what is the probability of getting exactly 3 heads ? 
Options: a ) 1 / 2 , b ) 1 / 4 , c ) 1 / 8 , d ) 1 / 16 , e ) 3 / 16
Output: b
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 ? 
Options: a ) 30 , b ) 60 , c ) 90 , d ) 180 , e ) 540
Output: c
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 ? 
Options: a ) 3 / 40000 , b ) 1 / 1000 , c ) 9 / 2000 , d ) 1 / 60 , e ) 1 / 15
Output: b
Problem: there are 24 students in a class . in how many different ways can a committee of 3 students be formed ? 
Options: a ) 1250 , b ) 1800 , c ) 2024 , d ) 3256 , e ) 2864
Output: c
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 ? 
Options: a ) 1 / 3 , b ) 2 / 3 , c ) 2 / 7 , d ) 3 / 11 , e ) 4 / 5
Output: c
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 . 
Options: a ) 1 / 64 , b ) 1 / 36 , c ) 1 / 12 , d ) 1 / 6 , e ) 1 / 3
Output: a