niryuu/sni-each-converted huggingface dataset:
Problem: there is a 20 % chance sandy will visit china this year , while there is a 60 % chance that she will visit malaysia this year . what is the probability that sandy will visit either china or malaysia this year , but not both ? 
Options: a ) 40 % , b ) 48 % , c ) 56 % , d ) 64 % , e ) 72 %
Output: c
Problem: a certain junior class has 1,000 students and a certain senior class has 800 students . among these students , there are 20 siblings pairs , each consisting of 1 junior and 1 senior . if 1 student is to be selected at random from each class , what is the probability that the 2 students selected at will be a sibling pair ? 
Options: a ) 3 / 40,000 , b ) 1 / 3,600 , c ) 9 / 2,000 , d ) 1 / 40,000 , e ) 1 / 15
Output: d
Problem: the membership of a committee consists of 4 english teachers , 2 mathematics teachers , and 2 social studies teachers . if 2 committee members are to be selected at random to write the committee ’ s report , what is the probability that the two members selected will both be english teachers ? 
Options: a ) 2 / 3 , b ) 1 / 3 , c ) 2 / 9 , d ) 1 / 12 , e ) 3 / 28
Output: e
Problem: x , y , and z are all unique numbers . if x is chosen randomly from the set { 8 , 9 , 10 , 11 } and y and z are chosen randomly from the set { 20 , 21 , 22 , 23 } , what is the probability that x and y are prime and z is not ? 
Options: a ) 1 / 16 , b ) 3 / 11 , c ) 13 / 20 , d ) 3 / 10 , e ) 1 / 10
Output: a
Problem: a child want to buy 5 new toys . if there are 15 toys that satisfy the child ' s criteria , in how many different ways can the child select the 5 new toys if the order of selection does n ' t matter . 
Options: a ) 210 , b ) 1365 , c ) 3003 , d ) 5005 , e ) 3030
Output: c
Problem: three coins are tossed . find the probability of at least 2 tails ? 
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 1 / 4 , d ) 1 / 8 , e ) 3 / 8
Output: a
Problem: jane and thomas are among the 6 people from which a committee of 3 people is to be selected . how many different possible committees of 3 people can be selected from these 6 people if at least one of either jane or thomas is to be selected ? 
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Output: c
Problem: a meeting has to be conducted with 5 managers . find the number of ways in which the managers may be selected from among 7 managers , if there are 2 managers who refuse to attend the meeting together . 
Options: a ) 6 , b ) 8 , c ) 10 , d ) 11 , e ) 15
Output: d
Problem: in how many ways 4 boys and 5 girls can be seated in a row so that they are alternate . 
Options: a ) 144 , b ) 288 , c ) 12 , d ) 256 , e ) 2880
Output: e
Problem: two mba admissions committees are to be formed randomly from 6 second year mbas with 3 members each . what is the probability e that jane will be on the same committee as albert ? 
Options: a ) 12 % , b ) 20 % , c ) 33 % , d ) 40 % , e ) 50 %
Output: d
Problem: the chance of rain on any given day in tel - aviv is 50 % . what is the probability q that it rained in tel - aviv on exactly 4 out of 6 randomly chosen days ? 
Options: a ) 15 / 64 , b ) 30 / 64 , c ) 1 / 2 , d ) 1 / 4 , e ) 52 / 64
Output: a
Problem: a fair coin is tossed 5 times . what is the probability of getting more heads than tails in 5 tosses ? 
Options: a ) 1 / 2 , b ) 63 / 128 , c ) 4 / 7 , d ) 61 / 256 , e ) 63 / 64
Output: a
Problem: a bag contains 3 red , 5 yellow and 4 green balls . 3 balls are drawn randomly . what is the probability that balls drawn contain exactly two green balls ? 
Options: a ) 9 / 16 , b ) 7 / 18 , c ) 12 / 55 , d ) 14 / 67 , e ) 19 / 87
Output: c
Problem: kim has 3 pairs of shoes ; each pair is a different color . if kim randomly selects 2 shoes without replacement from the 6 shoes , what is the probability that she will select 2 shoes of the same color ? 
Options: a ) 2 / 5 , b ) 1 / 5 , c ) 1 / 9 , d ) 1 / 10 , e ) 1 / 25
Output: b
Problem: there are 13 boys and 10 girls in a class . if three students are selected at random , in how many ways that 1 girl & 2 boys are selected ? 
Options: a ) 120 , b ) 480 , c ) 780 , d ) 720 , e ) 800
Output: c
Problem: joe has candys on his pocket , 4 of those candies have lemon flavor , and 3 have caramel flavor . if joe take one , what is the probability that he picks one caramel flavor ? 
Options: a ) 1 , b ) 2 , c ) none , d ) 3 / 7 , e ) 3 / 4
Output: d
Problem: there is a 50 % chance jen will visit chile this year , while there is a 50 % chance that she will visit madagascar this year . what is the probability that jen will visit either chile or madagascar this year , but not both ? 
Options: a ) 25.0 % , b ) 50.0 % , c ) 62.5 % , d ) 75.0 % , e ) 80.0 %
Output: b
Problem: what is the probability that the sum of two dice will yield a 5 , and then when both are thrown again , their sum will again yield a 5 ? assume that each die has 4 sides with faces numbered 1 to 4 . 
Options: a ) 1 / 144 , b ) 1 / 36 , c ) 1 / 12 , d ) 1 / 16 , e ) 1 / 3
Output: d
Problem: wink , inc . follows a certain procedure that requires two tasks to be finished independently in order for a job to be done . on any given day , there is a 5 / 8 probability that task 1 will be completed on time , and a 3 / 5 probability that task 2 will be completed on time . on a certain day , what is the probability that task 1 will be completed on time , but task 2 will not ? 
Options: a ) 1 / 4 , b ) 3 / 40 , c ) 13 / 40 , d ) 7 / 20 , e ) 13 / 22
Output: a
Problem: two unbiased coins are tossed . what is the probability of getting at most one head ? 
Options: a ) 2 / 3 , b ) 1 , c ) 3 / 4 , d ) 2 , e ) 1 / 2
Output: c
Problem: there are 8 books on a shelf , of which 3 are paperbacks and 5 are hardbacks . how many possible selections of 4 books from this shelf include at least one paperback ? 
Options: a ) a ) 40 , b ) b ) 45 , c ) c ) 50 , d ) d ) 55 , e ) e ) 65
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 4 bottles of apple juice among the 6 bottles ? assume that every bottle has an equal chance of being bought . 
Options: a ) 2 / 5 , b ) 3 / 5 , c ) 2 / 3 , d ) 1 / 2 , e ) 3 / 7
Output: e
Problem: five 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 / 1296 , c ) 1 / 33 , d ) 1 / 38 , e ) 1 / 34
Output: b
Problem: what is the probability that a two digit number selected at random will be a multiple of ' 3 ' and not a multiple of ' 5 ' ? 
Options: a ) 2 / 15 , b ) 4 / 15 , c ) 1 / 15 , d ) 4 / 90 , e ) 5 / 60
Output: b
Problem: what is the probability of getting a sum of 12 when rolling 3 dice simultaneously ? 
Options: a ) 10 / 216 , b ) 12 / 216 , c ) 21 / 216 , d ) 23 / 216 , e ) 25 / 216
Output: e
Problem: lola rolls a die 3 times . what is the probability that she gets a 4 on the last one of the 3 rolls ? 
Options: a ) 215 / 216 , b ) 216 , c ) 1 / 216 , d ) none , e ) 2
Output: a
Problem: find the probability that a year chosen at random has 53 mondays . 
Options: a ) 5 / 28 , b ) 3 / 28 , c ) 1 / 28 , d ) 3 / 28 , e ) 3 / 27
Output: a
Problem: if 4 people are selected from a group of 6 married couples , what is the probability that none of them would be married to each other ? 
Options: a ) 1 / 33 , b ) 2 / 33 , c ) 1 / 3 , d ) 16 / 33 , e ) 11 / 12
Output: d
Problem: if a coin is flipped , the probability that the coin will land heads is 1 / 2 . if the coin is flipped 6 times , what is the probability that it will land heads up on all 6 flips ? 
Options: a ) 1 / 6 , b ) 1 / 8 , c ) 1 / 32 , d ) 1 / 2 , e ) 1 / 64
Output: e
Problem: what is the probability of getting exactly 4 heads 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: if two integers x , y ( x > y ) are selected from - 10 to 11 ( inclusive ) , how many possible cases are there ? 
Options: a ) 150 , b ) 180 , c ) 190 , d ) 210 , e ) 231
Output: e
Problem: find the probability that a leap year selected at random will have 53 sundays 
Options: a ) 6 / 7 , b ) 5 / 7 , c ) 4 / 7 , d ) 3 / 7 , e ) 2 / 7
Output: e
Problem: there are 10 pairs of socks and 2 socks are worn from that such that the pair of socks worn are not of the same pair . what is the number of pair that can be formed . 
Options: a ) 90 , b ) 85 , c ) 75 , d ) 95 , e ) 82
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 5 or 12 ? 
Options: a ) 17 / 30 , b ) 2 / 5 , c ) 7 / 15 , d ) 4 / 15 , e ) 11 / 30
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 200 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 ) 170
Output: b
Problem: a life insurance company insured 25,000 young boys , 14,000 young girls and 16,000 young adults . the probability of death within 10 years of a young boy , young girl and a young adult are 0.02 , 0.03 and 0.15 respectively . one insured person dies . what is the probability that the dead person is a young boy ? 
Options: a ) 36 / 165 , b ) 25 / 166 , c ) 26 / 165 , d ) 32 / 165 , e ) 33 / 165
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 z 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: from a pack of 52 cards , 1 card is drawn at random . what is the probability that a jack , queen , or king is drawn ? 
Options: a ) 1 / 4 , b ) 1 / 12 , c ) 2 / 13 , d ) 3 / 13 , e ) 3 / 26
Output: d
Problem: a jar contains 5 black and 2 white balls . if you pick two balls at the same time , what ' s the probability that one ball is black and one is white ? 
Options: a ) 2 / 7 , b ) 5 / 21 , c ) 4 / 21 , d ) 3 / 7 , e ) 1 / 2
Output: b
Problem: a bag consists of 20 marbles , of which 5 are blue , 9 are red , and the remainder are white . if lisa is to select a marble from the bag at random , what is the probability that the marble will be red or white ? 
Options: a ) 3 / 4 , b ) 2 / 4 , c ) 1 / 4 , d ) 1 / 8 , e ) 1 / 16
Output: a
Problem: from a pack of 52 cards , two cards are drawn together at random . what is the probability that the one is heart and other two is diamond ? 
Options: a ) 238 / 5525 , b ) 176 / 5534 , c ) 253 / 5523 , d ) 234 / 5525 , e ) 1 / 5525
Output: d
Problem: how many cubes of 4 cm edge can be cut out of a cube of 28 cm edge 
Options: a ) 343 , b ) 232 , c ) 216 , d ) 484 , e ) none of these
Output: a
Problem: from a pack of 52 cards , two cards are drawn together at random . what is the probability of one is a spade and one is a heart ? 
Options: a ) 102 / 102 , b ) 5 / 102 , c ) 1 / 102 , d ) 8 / 102 , e ) 13 / 102
Output: e
Problem: there are 7 red shoes & 3 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 / 15 , d ) 7 / 15 , e ) 7 / 16
Output: d
Problem: x , y , and z are all unique numbers . if x is chosen randomly from the set { 9 , 10 , 11 } and y and z are chosen randomly from the set { 20 , 21 , 22 , 23 } , what is the probability that x and y are prime and z is not ? 
Options: a ) 1 / 20 , b ) 1 / 12 , c ) 2 / 15 , d ) 3 / 10 , e ) 1 / 7
Output: b
Problem: a coin is tossed twice if the coin shows head it is tossed again but if it shows a tail then a die is tossed . if 8 possible outcomes are equally likely . find the probability that the die shows a number greater than 4 , if it is known that the first throw of the coin results in a tail 
Options: a ) 2 / 4 , b ) 1 / 3 , c ) 2 / 3 , d ) 3 / 6 , e ) 1 / 4
Output: b
Problem: there are 10 students named alphabetically from a to j . what is the probability that a and d do not sit together if all 10 sit around a circular table ? 
Options: a ) 2 / 9 , b ) 2 / 5 , c ) 7 / 9 , d ) 4 / 5 , e ) 8 / 9
Output: c
Problem: there are 7 red balls and 5 blue balls in a jar . if 3 balls are selected from the jar , what is the probability that 3 balls selected are red balls ? 
Options: a ) 19 / 44 , b ) 5 / 44 , c ) 3 / 41 , d ) 13 / 44 , e ) 7 / 44
Output: e
Problem: a question paper has 2 parts , a & b , each containing 10 questions . if a student has to choose 5 from part a & 10 from part b , in how many ways can he choose the questions ? 
Options: a ) 100 , b ) 120 , c ) 125 , d ) 350 , e ) 252
Output: e
Problem: what is the probability of drawing a queen from a deck of 52 cards ? 
Options: a ) 4 / 13 , b ) 1 / 13 , c ) 4 , d ) 1 , e ) 2 / 13
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 700 newborn members of the population , approximately how many would be expected to survive the first 3 months of life ? 
Options: a ) 511 , b ) 546 , c ) 552 , d ) 562 , e ) 570
Output: a
Problem: if 4 people are selected from a group of 9 married couples , what is the probability that none of them would be married to each other ? 
Options: a ) 1 / 33 , b ) 2 / 85 , c ) 1 / 3 , d ) 56 / 85 , e ) 11 / 85
Output: d
Problem: what is the probability of getting a sum 9 from two throws of a dice ? 
Options: a ) 1 / 6 , b ) 1 / 8 , c ) 1 / 9 , d ) 1 / 12 , e ) none of these
Output: c
Problem: a father purchased dress for his 3 daughters . the dresses are of same color but diff size and they are kept in dark room . what is probability that all the 3 will not choose there own dress ? 
Options: a ) 1 / 3 , b ) 2 / 3 , c ) 1 / 2 , d ) 3 / 4 , e ) 3 / 7
Output: a
Problem: there are 13 clubs in a full deck of 52 cards . in a certain game , you pick a card from a standard deck of 52 cards . if the card is a club , you win . if the card is not a club , the person replaces the card to the deck , reshuffles , and draws again . the person keeps repeating that process until he picks a club , and the point is to measure how many draws it took before the person picked a club and , thereby , won . what is the probability that one will pick the first club on the forth draw or later ? 
Options: a ) 1 / 2 , b ) 3 / 4 , c ) 7 / 8 , d ) 27 / 32 , e ) 27 / 64
Output: e
Problem: three unbiased coins are tossed . what is the probability of getting 2 heads and 2 tail ? 
Options: a ) 5 / 8 , b ) 1 / 4 , c ) 3 / 8 , d ) 7 / 8 , e ) 1 / 8
Output: a
Problem: preethi has 6 flavors of ice cream in his parlor . how many options are there for dorathy to pick a one - flavor , two - flavor , 3 - flavor , 4 - flavor , 5 flavor or 6 flavor order ? 
Options: a ) 26 , b ) 36 , c ) 64 , d ) 67 , e ) 63
Output: e
Problem: what is the probability of getting at least one six in a single throw of three unbiased dice ? 
Options: a ) 1 / 6 , b ) 125 / 216 , c ) 1 / 36 , d ) 81 / 216 , e ) 91 / 216
Output: e
Problem: what is the sum of all 5 digit numbers which can be formed with the digits 0 , 1,2 , 3,4 without repetation ? 
Options: a ) 2599980 , b ) 235500 , c ) 923580 , d ) 765432 , e ) 765434
Output: a
Problem: if a coin is flipped , the probability that the coin will land tails is 1 / 2 . if the coin is flipped 3 times , what is the probability that it will land tails up on the first flip and not on the last 2 flips ? 
Options: a ) 1 / 8 , b ) 1 / 4 , c ) 1 / 3 , d ) 1 / 2 , e ) 3 / 4
Output: a
Problem: 45 girls and 60 boys are present at a party . there are 17 girl - boy are in relationship among them . if a girl and a boy is selected at random , what is the probability that they will be not a couple ? 
Options: a ) 17 / 2900 , b ) 2683 / 2700 , c ) 2496 / 2700 , d ) 2369 / 2700 , e ) 198 / 270
Output: b
Problem: what is the probability of getting a sum 9 from two throw of a dice ? 
Options: a ) 1 / 6 , b ) 1 / 8 , c ) 1 / 9 , d ) 1 / 12 , e ) 1 / 13
Output: c
Problem: if two integers x , y ( x > y ) are selected from - 10 to 5 ( inclusive ) , how many possible cases are there ? 
Options: a ) 105 , b ) 120 , c ) 190 , d ) 210 , e ) 240
Output: b
Problem: there are 6 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 / 4 , c ) 1 / 2 , d ) 1 / 5 , e ) 1 / 6
Output: a
Problem: a certain junior class has 100 students and a certain senior class has 80 students . among these students , there are 6 siblings pairs each consisting of 1 junior and 1 senior . if 1 student is to be selected at random from each class , what is the probability that the 2 students selected will be a sibling pair ? 
Options: a ) 3 / 40000 , b ) 1 / 3600 , c ) 9 / 2000 , d ) 3 / 4000 , e ) 1 / 15
Output: d
Problem: two 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 / 6 , c ) 1 / 33 , d ) 1 / 38 , e ) 1 / 34
Output: b
Problem: a jar contains only red , yellow , and orange marbles . if there are 3 red , 5 yellow , and 4 orange marbles , and 2 marbles are chosen from the jar at random without replacing any of them , what is the probability that 2 yellow , 1 red , and no orange marbles will be chosen ? 
Options: a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 6 / 22
Output: e
Problem: the membership of a committee consists of 3 english teachers , 4 mathematics teachers , and 2 social studies teachers . if 2 committee members are to be selected at random to write the committee ’ s report , what is the probability that the two members selected will both be maths teachers ? 
Options: a ) 2 / 3 , b ) 1 / 3 , c ) 2 / 9 , d ) 1 / 24 , e ) 1 / 12
Output: e
Problem: find the probability that a number selected from numbers 1 , 2 , 3 , . . . , 50 is a prime number , when each of the given numbers is equally likely to be selected ? 
Options: a ) 10 / 50 , b ) 15 / 50 , c ) 8 / 50 , d ) 3 / 50 , e ) 7 / 50
Output: b
Problem: the probability that a number selected at random from the first 100 natural numbers is a composite number is ? 
Options: a ) 2 / 3 , b ) 3 / 5 , c ) 3 / 4 , d ) 3 / 2 , e ) 5 / 2
Output: d
Problem: from a group of 3 women and 3 girls , 4 are to be randomly selected . what is the probability that equal numbers of women and girls will be selected ? 
Options: a ) 3 / 5 , b ) 1 / 5 , c ) 2 / 5 , d ) 4 / 5 , e ) 1
Output: a
Problem: how many positive integers less than 300 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: b
Problem: the maitre ' d at an expensive manhattan restaurant has noticed that 60 % of the couples order dessert and coffee . however , 20 % of the couples who order dessert do n ' t order coffee . what is the probability t that the next couple the maitre ' d seats will not order dessert ? 
Options: a ) 20 % , b ) 25 % , c ) 40 % , d ) 60 % , e ) 75 %
Output: b
Problem: a bag contains 5 white marbles and 5 black marbles . if each of 5 girls and 5 boys randomly selects and keeps a marble , what is the probability that all of the girls select the same colored marble ? 
Options: a ) 1 / 126 , b ) 1 / 120 , c ) 1 / 24 , d ) 4 / 25 , e ) 1 / 2
Output: a
Problem: if two integers x , y ( x > y ) are selected from - 10 to 4 ( inclusive ) , how many possible cases are there ? 
Options: a ) 150 , b ) 180 , c ) 190 , d ) 210 , e ) 105
Output: e
Problem: 30 ladies and 60 gentlemen are present at a party . there are 23 couples among them . if a lady and a gentleman is selected at random , what is the probability that they will be a couple ? 
Options: a ) 1 / 200 , b ) 1 / 100 , c ) 1 / 50 , d ) 1 / 40 , e ) 23 / 1800
Output: e
Problem: there are 3 pairs of socks and 2 socks are worn from that such that the pair of socks worn are not of the same pair . what is the number of pair that can be formed . 
Options: a ) 5 , b ) 1 , c ) 3 , d ) 6 , e ) 7
Output: d
Problem: in how many ways 5 boys and 5 girls can be seated in a row so that boys and girls are alternate ? 
Options: a ) 28400 , b ) 28500 , c ) 28600 , d ) 28700 , e ) 28800
Output: e
Problem: what is the probability that the sum of two dice will yield a 7 , and then when both are thrown again , their sum will again yield a 7 ? assume that each die has 6 sides with faces numbered 1 to 6 . 
Options: a ) 1 / 144 , b ) 1 / 36 , c ) 1 / 12 , d ) 1 / 6 , e ) 1 / 3
Output: b
Problem: a string of 50 light bulbs is wired in such a way that if any individual light bulb fails , the entire string fails . if for each individual light bulb the probability of failing during time period t is 0.05 , what is the probability that the string of light bulbs will fail during the time period t ? 
Options: a ) 0.05 , b ) ( 0.05 ) ^ 50 , c ) 1 - ( 0.96 ) ^ 50 , d ) 1 - ( 0.95 ) ^ 50 , e ) ( 0.95 ) ^ 50
Output: d
Problem: in a throw of dice what is the probability of ge æ « ng number greater than 2 
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 1 / 5 , d ) 1 / 6 , e ) none of these
Output: b
Problem: in a throw of dice what is the probability of ge æ « ing number greater than 2 
Options: a ) 2 / 3 , b ) 1 / 3 , c ) 1 / 5 , d ) 1 / 6 , e ) none of these
Output: a
Problem: in how many ways 6 boys and 6 girls can be seated in a row so that boys and girls are alternate ? 
Options: a ) 1063800 , b ) 1083600 , c ) 1036800 , d ) 1053800 , e ) 1073600
Output: c
Problem: a certain junior class has 1000 students and a certain senior class has 800 students . among these students , there are 40 siblings pairs each consisting of 1 junior and 1 senior . if 1 student is to be selected at random from each class , what is the probability that the 2 students selected will be a sibling pair ? 
Options: a ) 3 / 40000 , b ) 1 / 3600 , c ) 1 / 20000 , d ) 1 / 60 , e ) 1 / 15
Output: c
Problem: if two integers x , y ( x > y ) are selected from - 10 to 1 ( inclusive ) , how many possible cases are there ? 
Options: a ) 150 , b ) 66 , c ) 190 , d ) 210 , e ) 240
Output: b
Problem: what is the probability of getting a sum of 8 or 14 when rolling 3 dice simultaneously ? 
Options: a ) 1 / 6 , b ) 1 / 4 , c ) 1 / 2 , d ) 21 / 216 , e ) 32 / 216
Output: a
Problem: from a group of 5 boys and 5 girls , 6 children are to be randomly selected . what is the probability that 3 boys and 3 girls will be selected ? 
Options: a ) 4 / 15 , b ) 6 / 17 , c ) 8 / 19 , d ) 10 / 21 , e ) 12 / 23
Output: d
Problem: a box contains 21 electric bulbs , out of which 4 are defective . two bulbs are chosen at random from this box . the probability that at least one of these is defective is 
Options: a ) 4 / 19 , b ) 7 / 19 , c ) 12 / 19 , d ) 21 / 95 , e ) 31 / 88
Output: e
Problem: a coin is tossed six times . what is the probability that there is at the least one tail ? 
Options: a ) 63 / 64 , b ) 31 / 37 , c ) 31 / 18 , d ) 31 / 10 , e ) 31 / 19
Output: a
Problem: the maitre ' d at an expensive manhattan restaurant has noticed that 60 % of the couples order dessert and coffee . however , 20 % of the couples who order dessert do n ' t order coffee . what is the probability w that the next couple the maitre ' d seats will not order dessert ? 
Options: a ) 20 % , b ) 25 % , c ) 40 % , d ) 60 % , e ) 75 %
Output: b
Problem: a bag consists of 30 marbles , of which 5 are blue , 9 are red , and the remainder are white . if lisa is to select a marble from the bag at random , what is the probability that the marble will be red or white ? 
Options: a ) 5 / 6 , 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 alternate . 
Options: a ) 144 , b ) 288 , c ) 12 , d ) 256 , e ) none
Output: a
Problem: how many different ways can 2 students be seated in a row of 5 desks , so that there is always at least one empty desk between the students ? 
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 12
Output: e
Problem: there are 5 red shoes & 4 green shoes . if two of red shoes are drawn what is the probability of getting red shoes 
Options: a ) 1 / 18 , b ) 1 / 14 , c ) 5 / 18 , d ) 1 / 15 , e ) 1 / 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 400 newborn members of the population , approximately how many would be expected to survive the first 3 months of life ? 
Options: a ) 240 , b ) 246 , c ) 252 , d ) 292 , e ) 298
Output: d
Problem: when 3 fair coins are tossed together , what is the probability of getting 2 tails ? 
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 3 / 4 , e ) 2 / 3
Output: a
Problem: if g is to be chosen at random from the set { 5,8 , 7,1 } and k is to be chosen at random from the set { 14 , 8,3 } , what is the probability that gk will be even ? 
Options: a ) 1 , b ) 5 , c ) 8 , d ) 4 , e ) 3
Output: a
Problem: a box contains 20 electric bulbs , out of which 4 are defective . two bulbs are chosen at random form this box . the probability that at least one of these is defective is : 
Options: a ) 8 / 19 , b ) 7 / 19 , c ) 10 / 19 , d ) 20 / 19 , e ) 22 / 19
Output: b
Problem: if 4 people are selected from a group of 8 married couples , what is the probability that none of them would be married to each other ? 
Options: a ) 1 / 33 , b ) 2 / 33 , c ) 8 / 13 , d ) 16 / 33 , e ) 11 / 12
Output: c
Problem: 3.00001 unbiased coins are tossed . what is the probability of getting 2 tails ? 
Options: a ) 3 / 4 , b ) 1 / 4 , c ) 3 / 8 , d ) 7 / 8 , e ) 1 / 8
Output: c
Problem: in how many ways 4 boys and 1 girls can be seated in a row so that they are alternate . 
Options: a ) 144 , b ) 288 , c ) 24 , d ) 256 , e ) none
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 3 / 8 probability that task 1 will be completed on time , and a 3 / 5 probability that task 2 will be completed on time . on a certain day , what is the probability that task 1 will be completed on time , but task 2 will not ? 
Options: a ) 1 / 20 , b ) 3 / 40 , c ) 13 / 40 , d ) 3 / 20 , e ) 13 / 22
Output: d
Problem: 5 letters have to be put in 5 different envelopes numbered 1 through 5 such that each of the letters go into only 1 envelope . the letter is said to be put in correct position if for example letter 1 goes into envelope 1 . now what is the probability that all letters be put into wrong envelopes ? 
Options: a ) 1 / 3 , b ) 2 / 3 , c ) 11 / 120 , d ) 11 / 30 , e ) 76 / 120
Output: d
Problem: there is a 50 % chance jen will visit chile this year , while there is a 25 % chance that she will visit madagascar this year . what is the probability that jen will visit either chile or madagascar this year , but not both ? [ / b ] 
Options: a ) 25 % , b ) 50 % , c ) 62.5 % , d ) 63.5 % , e ) 75 %
Output: b
Problem: kim has 5 pairs of shoes ; each pair is a different color . if kim randomly selects 2 shoes without replacement from the 10 shoes , what is the probability that she will select 2 shoes of the same color ? 
Options: a ) 2 / 5 , b ) 1 / 5 , c ) 1 / 9 , d ) 1 / 10 , e ) 1 / 25
Output: c
Problem: a fair coin is tossed 11 times . what is the probability of getting more heads than tails in 11 tosses ? 
Options: a ) 1 / 2 , b ) 63 / 128 , c ) 4 / 7 , d ) 61 / 256 , e ) 63 / 64
Output: a
Problem: three unbiased coins are tossed . what is the probability of getting at least 2 tails ? 
Options: a ) 0.75 , b ) 0.5 , c ) 0.25 , d ) 0.2 , e ) 0.3
Output: b
Problem: a meeting has to be conducted with 4 managers . find the number of ways in which the managers be selected from among 7 managers , if 2 managers will not attend the meeting together ? 
Options: a ) 25 , b ) 20 , c ) 35 , d ) 36 , e ) 38
Output: a
Problem: bill and jane play a simple game involving two fair dice , each of which has 6 sides numbered from 1 to 6 ( with an equal chance of landing on any side ) . bill rolls the dice and his score is the total of the two dice . jane then rolls the dice and her score is the total of her two dice . if jane ’ s score is higher than bill ’ s , she wins the game . what is the probability the jane will win the game ? 
Options: a ) 15 / 36 , b ) 175 / 432 , c ) 575 / 1296 , d ) 583 / 1296 , e ) 1 / 2
Output: c
Problem: a jar contains 3 black , 3 white and 1 green balls . if you pick two balls at the same time , what ' s the probability that one ball is black and one is white ? 
Options: a ) 2 / 7 , b ) 5 / 7 , c ) 4 / 7 , d ) 3 / 7 , e ) 1 / 2
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 8 managers , if 2 managers will not attend the meeting together ? 
Options: a ) 40 , b ) 36 , c ) 42 , d ) 45 , e ) 47
Output: b
Problem: in 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 / 7 , b ) 2 / 7 , c ) 3 / 7 , d ) 4 / 7 , e ) 1
Output: b
Problem: how many different ways can 2 students be seated in a row of 3 desks , so that there is always at least one empty desk between the students ? 
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 12
Output: a
Problem: john and peter are among the 9 players a volleyball coach can choose from to field a 6 - player team . if all 6 players are chosen at random , what is the probability of choosing a team that includes john and peter ? 
Options: a ) 3 / 10 , b ) 4 / 11 , c ) 5 / 12 , d ) 6 / 13 , e ) 7 / 15
Output: c
Problem: three unbiased coins are tossed . what is the probability of getting 1 heads and 1 tail ? 
Options: a ) 3 / 4 , b ) 1 / 4 , c ) 3 / 8 , d ) 7 / 8 , e ) 1 / 8
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 q 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 4 attempts ? 
Options: a ) 3 / 4 , b ) 5 / 8 , c ) 7 / 8 , d ) 11 / 16 , e ) 15 / 16
Output: e
Problem: find the probability that a number selected from numbers 1 , 2 , 3 , . . . , 20 is a prime number , when each of the given numbers is equally likely to be selected ? 
Options: a ) 10 / 20 , b ) 1 / 20 , c ) 8 / 20 , d ) 3 / 20 , e ) 7 / 20
Output: c
Problem: two letters from the word barkhint are selected at random . what is the probability that at least one of the selected letters is a consonant ? 
Options: a ) 30 / 28 , b ) 40 / 28 , c ) 25 / 28 , d ) 27 / 28 , e ) 32 / 28
Output: d
Problem: a certain junior class has 3000 students and a certain senior class has 800 students . among these students , there are 60 siblings pairs each consisting of 1 junior and 1 senior . if 1 student is to be selected at random from each class , what is the probability that the 2 students selected will be a sibling pair ? 
Options: a ) 1 / 40000 , b ) 1 / 3600 , c ) 9 / 2000 , d ) 1 / 60 , e ) 1 / 15
Output: a
Problem: the maitre ' d at an expensive manhattan restaurant has noticed that 60 % of the couples order dessert and coffee . however , 20 % of the couples who order dessert do n ' t order coffee . what is the probability q that the next couple the maitre ' d seats will not order dessert ? 
Options: a ) 20 % , b ) 25 % , c ) 40 % , d ) 60 % , e ) 75 %
Output: b
Problem: there are 3 red shoes & 7 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 / 12 , d ) 1 / 15 , e ) 1 / 16
Output: d
Problem: a bag consists of 60 marbles , of which 5 are blue , 9 are red , and the remainder are white . if lisa is to select a marble from the bag at random , what is the probability that the marble will be red or white ? 
Options: a ) 11 / 12 , b ) 2 / 4 , c ) 1 / 4 , d ) 1 / 8 , e ) 1 / 16
Output: a
Problem: if a coin is flipped , the probability that the coin will land tails is 1 / 2 . if the coin is flipped 5 times , what is the probability that it will land tails up on the first 2 flips and not on the last 3 flips ? 
Options: a ) 3 / 5 , b ) 1 / 32 , c ) 1 / 5 , d ) 1 / 4 , e ) 1 / 2
Output: b
Problem: in how many ways can 7 boys be seated in a circular order ? 
Options: a ) 110 , b ) 230 , c ) 720 , d ) 420 , e ) 680
Output: c
Problem: there is a 75 % chance that tigers will not win at all during the whole season . there is a 25 % chance that germany will not play at all in the whole season . what is the greatest possible probability that the tigers will win and germany will play during the season ? 
Options: a ) 55 % , b ) 60 % , c ) 70 % , d ) 75 % , e ) 80 %
Output: d
Problem: the maitre ' d at an expensive manhattan restaurant has noticed that 60 % of the couples order dessert and coffee . however , 20 % of the couples who order dessert do n ' t order coffee . what is the probability y that the next couple the maitre ' d seats will not order dessert ? 
Options: a ) 20 % , b ) 25 % , c ) 40 % , d ) 60 % , e ) 75 %
Output: b
Problem: in how many ways can 21 books on english and 19 books on french be placed in a row on a shelf so that two books on french may not be together ? 
Options: a ) 3990 , b ) 1540 , c ) 1995 , d ) 3672 , e ) none of these
Output: b
Problem: from a pack of 52 cards , two cards are drawn at random together at random what is the probability of both the cards being kings ? 
Options: a ) 1 / 221 , b ) 8 / 221 , c ) 4 / 589 , d ) 4 / 587 , e ) 7 / 654
Output: a
Problem: two mba admissions committees are to be formed randomly from 6 second year mbas with 3 members each . what is the probability w that jane will be on the same committee as albert ? 
Options: a ) 12 % , b ) 20 % , c ) 33 % , d ) 40 % , e ) 50 %
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 600 newborn members of the population , approximately how many would be expected to survive the first 3 months of life ? 
Options: a ) 438 , b ) 446 , c ) 452 , d ) 462 , e ) 470
Output: a
Problem: a fair coin is tossed 5 times . what is the probability that it lands heads up at least twice ? 
Options: a ) 1 / 16 , b ) 5 / 16 , c ) 2 / 5 , d ) 13 / 16 , e ) 27 / 32
Output: d
Problem: kim has 6 pairs of shoes ; each pair is a different color . if kim randomly selects 2 shoes without replacement from the 12 shoes , what is the probability that she will select 2 shoes of the same color ? 
Options: a ) 2 / 5 , b ) 1 / 5 , c ) 1 / 9 , d ) 1 / 11 , e ) 1 / 25
Output: d
Problem: jane and thomas are among the 8 people from which a committee of 3 people is to be selected . how many different possible committees of 3 people can be selected from these 8 people if at least one of either jane or thomas is to be selected ? 
Options: a ) 24 , b ) 28 , c ) 32 , d ) 36 , e ) 40
Output: d
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 / 13 , b ) 2 / 13 , c ) 1 / 26 , d ) 1 / 52 , e ) 1 / 23
Output: c
Problem: three 6 faced dice are thrown together . the probability that no two dice show the same number on them is 
Options: a ) 5 / 0 , b ) 5 / 9 , c ) 5 / 1 , d ) 5 / 3 , e ) 5 / 6
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 r that jane will be on the same committee as albert ? 
Options: a ) 12 % , b ) 20 % , c ) 33 % , d ) 40 % , e ) 50 %
Output: d
Problem: an unbaised coin is tossed until it shows up the same face in 2 consicative throws wat is the probability that the no of tosses is not more than 4 . 
Options: a ) 3 / 4 , b ) 1 / 4 , c ) 7 / 8 , d ) 1 / 8 , e ) 6 / 8
Output: c
Problem: what is the probability of randomly selecting one of the shortest diagonals from all the diagonals of a regular 9 - sided polygon ) ? 
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 6 , e ) 1 / 9
Output: b
Problem: from a group of 4 boys and 4 girls , 6 children are to be randomly selected . what is the probability that 3 boys and 3 girls will be selected ? 
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 5 , d ) 4 / 7 , e ) 5 / 9
Output: d
Problem: how many cubes of 5 cm edge can be cut out of a cube of 20 cm edge 
Options: a ) 36 , b ) 64 , c ) 216 , d ) 484 , e ) none of these
Output: b
Problem: the probability is 1 / 2 that a certain coin turns up heads on any given toss . if the coin is tossed 6 times , what is the probability that the coin turns up tails on at least one of the tosses ? 
Options: a ) 15 / 16 , b ) 21 / 32 , c ) 31 / 32 , d ) 63 / 64 , e ) 51 / 64
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 { 5 , 6 } , 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: b
Problem: a bag contains 6 black and 7 white balls . one ball is drawn at random . what is the probability that the ball drawn is white ? 
Options: a ) 4 , b ) 4 / 3 , c ) 4 / 5 , d ) 4 / 9 , e ) 7 / 13
Output: e
Problem: three unbiased coins are tossed . what is the probability of getting all tails ? 
Options: a ) 7 / 8 , b ) 1 / 2 , c ) 3 / 8 , d ) 1 / 4 , e ) 1 / 8
Output: e
Problem: what is the probability that jamie and tom will get selected for a job they both applied for in a company , given that their chances of getting selected is 2 / 3 and 5 / 7 respectively ? 
Options: a ) 13 / 25 , b ) 2 / 5 , c ) 9 / 20 , d ) 11 / 20 , e ) 10 / 21
Output: e
Problem: a jar contains 4 black and 3 white balls . if you pick two balls at the same time , what ' s the probability that one ball is black and one is white ? 
Options: a ) 2 / 7 , b ) 5 / 7 , c ) 4 / 7 , d ) 3 / 7 , e ) 1 / 2
Output: c
Problem: how many positive integers less than 300 can be formed using the numbers 1 , 2 , 3 a for the digits ? 
Options: a ) 30 , b ) 52 , c ) 66 , d ) 68 , e ) 84
Output: a
Problem: from a pack of 52 cards , 1 card is drawn at random . what is the probability that a king is drawn ? 
Options: a ) 1 / 4 , b ) 4 / 13 , c ) 1 / 13 , d ) 3 / 26 , e ) 7 / 52
Output: c
Problem: in a throw of a coin find the probability of getting a head ? 
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 2 / 3 , e ) 2 / 5
Output: a
Problem: find the probability that a leap year selected at random will have 53 mondays 
Options: a ) 6 / 7 , b ) 5 / 7 , c ) 4 / 7 , d ) 3 / 7 , e ) 2 / 7
Output: e
Problem: the probability that event a occurs is 0.4 , and the probability that event b occurs is 0.45 . if the probability that either event a or event b occurs is 0.6 , what is the probability that event b and event b will occur ? 
Options: a ) 0.25 , b ) 0.15 , c ) 0.45 , d ) 0.5 , e ) 0.55
Output: a
Problem: a coin is tossed 6 times . what is the probability of getting exactly 5 heads ? 
Options: a ) 3 / 8 , b ) 3 / 16 , c ) 5 / 16 , d ) 3 / 32 , e ) 7 / 64
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 / 6 . for a group of 200 newborn members of the population , approximately how many would be expected to survive the first 3 months of life ? 
Options: a ) 116 , b ) 146 , c ) 152 , d ) 162 , e ) 170
Output: a
Problem: three unbiased coins are tossed . what is the probability of getting at most 2 heads ? 
Options: a ) 7 / 8 , b ) 5 / 8 , c ) 3 / 8 , d ) 7 / 5 , e ) 3 / 5
Output: a
Problem: there is a 20 % chance sandy will visit china this year , while there is a 70 % chance that she will visit malaysia this year . what is the probability that sandy will visit either china or malaysia this year , but not both ? 
Options: a ) 44 % , b ) 48 % , c ) 54 % , d ) 62 % , e ) 70 %
Output: d
Problem: 4 dice are thrown simultaneously on the board . find the probability which show the same face ? 
Options: a ) 2 / 113 , b ) 3 / 117 , c ) 1 / 216 , d ) 3 / 111 , e ) 4 / 121
Output: c
Problem: if a certain coin is flipped , the probability that the coin will land heads is 1 / 2 . if the coin is flipped 5 times , what is the probability that it will land heads up on the first flip but not on the last 4 flips ? 
Options: a ) 1 / 4 , b ) 1 / 8 , c ) 1 / 16 , d ) 1 / 32 , e ) 1 / 64
Output: d
Problem: there are 22 students in a class . in how many different ways can a committee of 3 students be formed ? 
Options: a ) 1180 , b ) 1320 , c ) 1540 , d ) 1760 , e ) 1920
Output: c
Problem: a box contains 100 balls , numbered from 1 to 100 . if 3 balls are selected at random and with replacement from the box . if the 3 numbers on the balls selected contain two odd and one even . what is the probability l that the first ball picked up is odd numbered ? 
Options: a ) 0 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 1
Output: d
Problem: there is a 30 % chance jen will visit chile this year , while there is a 50 % chance that she will visit madagascar this year . what is the probability that jen will visit either chile or madagascar this year , but not both ? 
Options: a ) 25.0 % , b ) 37.5 % , c ) 50.0 % , d ) 62.5 % , e ) 75 %
Output: c
Problem: 4 dice are thrown simultaneously on the board . find the probability show the same face ? 
Options: a ) 2 / 113 , b ) 1 / 215 , c ) 1 / 216 , d ) 3 / 113 , e ) 4 / 113
Output: c
Problem: the probability that a number selected at random from the first 50 natural numbers is a composite number is 
Options: a ) 17 / 26 , b ) 17 / 25 , c ) 17 / 20 , d ) 17 / 22 , e ) 17 / 21
Output: b
Problem: a box contains 24 electric bulbs , out of which 4 are defective . two bulbs are chosen at random from this box . the probability that at least one of these is defective is 
Options: a ) 4 / 19 , b ) 7 / 19 , c ) 12 / 19 , d ) 24 / 77 , e ) none
Output: d
Problem: what is the probability of having 53 fridays in an ordinary year 
Options: a ) 1 / 5 , b ) 1 / 6 , c ) 1 / 7 , d ) 1 / 8 , e ) 1 / 9
Output: c
Problem: a , b , c , d , e sitting in a row what is the probability that a & b sitting adjacent . 
Options: a ) 1 / 5 , b ) 2 / 5 , c ) 3 / 5 , d ) 4 / 5 , e ) 6 / 5
Output: b
Problem: what is the probability of getting sum of 10 on rolling three dices ? 
Options: a ) 28 / 216 , b ) 27 / 216 , c ) 29 / 216 , d ) 26 / 216 , e ) 25 / 216
Output: b
Problem: a bag contains 20 red jellybeans and 20 blue jellybeans . if 3 jellybeans are removed one at a time , at random and are not replaced , what is the probability that all 3 jellybeans removed from the bag are blue ? 
Options: a ) 9 / 100 , b ) 2 / 19 , c ) 1 / 8 , d ) 3 / 20 , e ) 3 / 10
Output: d
Problem: what is the probability that the sum of two dice will yield a 4 , and then when both are thrown again , their sum will again yield a 4 ? assume that each die has 3 sides with faces numbered 1 to 3 . 
Options: a ) 1 / 144 , b ) 1 / 36 , c ) 1 / 9 , d ) 1 / 6 , e ) 1 / 3
Output: c
Problem: what is the probability of randomly selecting an arrangement of the letters of the word ` ` mediterranean ' ' in which the first letter is e and the last letter is r ? 
Options: a ) 1 / 13 , b ) 1 / 20 , c ) 1 / 26 , d ) 1 / 50 , e ) 1 / 100
Output: c
Problem: three unbiased coins are tossed . what is the probability of getting at most two heads ? 
Options: a ) 3 / 4 , b ) 1 / 4 , c ) 3 / 8 , d ) 7 / 8 , e ) none of these
Output: d
Problem: in a garden , there are yellow and green flowers which are straight and curved . if the probability of picking a green flower is 1 / 6 and picking a straight flower is 1 / 2 , then what is the probability of picking a flower which is yellow and straight 
Options: a ) 1 / 7 , b ) 1 / 8 , c ) 1 / 4 , d ) 3 / 7 , e ) 7 / 8
Output: d
Problem: what is the probability of drawing a ` ` queen ' ' from a deck of 52 cards ? 
Options: a ) 2 / 7 , b ) 1 / 13 , c ) 3 / 5 , d ) 2 / 8 , e ) 1 / 7
Output: b
Problem: three 6 faced dice are thrown together . the probability that all the three show the same number on them is - . 
Options: a ) 1 / 36 , b ) 1 / 216 , c ) 1 / 48 , d ) 1 / 55 , e ) 1 / 90
Output: a
Problem: a gardener is going to plant 2 red rosebushes and 2 white rosebushes . if the gardener is to select each of the bushes at random , one at a time , and plant them in a row , what is the probability that the 2 rosebushes in the middle of the row will be the red rosebushes ? 
Options: a ) 1 / 12 , b ) 1 / 6 , c ) 1 / 5 , d ) 1 / 3 , e ) ½
Output: b
Problem: if you roll one fair 6 - sided die , what is the probability that the number is even or less than 3 ? 
Options: a ) 2 / 3 , b ) 1 / 2 , c ) 3 / 4 , d ) 5 / 6 , e ) 1 / 3
Output: a
Problem: if you keep rolling a pair of dice together till a sum of 5 or 7 is obtained , then what is the probability that a sum of 5 comes before a sum of 7 ? 
Options: a ) 5 / 5 , b ) 4 / 5 , c ) 3 / 5 , d ) 2 / 5 , e ) 1 / 5
Output: d
Problem: if 4 consecutive letters are selected at random from the english alphabet , then the probability that one of the letters is a vowel is ? 
Options: a ) 13 / 23 , b ) 16 / 23 , c ) 11 / 23 , d ) 17 / 23 , e ) 18 / 23
Output: d
Problem: a box contains 2 red balls and 5 black balls . one by one , every ball is selected at random without replacement . what is the probability that the fourth ball selected is black ? 
Options: a ) 1 / 4 , b ) 7 / 5 , c ) 1 / 2 , d ) 5 / 8 , e ) 2 / 3
Output: b
Problem: a bag contains 6 black and 3 white balls . one ball is drawn at random . what is the probability that the ball drawn is white ? 
Options: a ) 3 / 4 , b ) 1 / 3 , c ) 1 / 7 , d ) 1 / 8 , e ) 4 / 3
Output: b
Problem: two cards are drawn together from a pack of 52 cards the probability that one is the spade and one is a heart is ? 
Options: a ) 85 / 852 , b ) 45 / 69 , c ) 18 / 456 , d ) 13 / 102 , e ) 23 / 125
Output: d
Problem: in a lottery there are 20 prizes and 35 blanks . a lottery is drawn at random . what is the probability of getting a prize 
Options: a ) 2 / 13 , b ) 4 / 11 , c ) 5 / 11 , d ) 6 / 11 , e ) 3 / 13
Output: b
Problem: in how many ways 4 boys and 2 girls can be seated in a row so that they are alternate . 
Options: a ) 48 , b ) 288 , c ) 12 , d ) 256 , e ) none
Output: a
Problem: find the probability that a leap year selected at random will not have 53 sundays or mondays . 
Options: a ) 6 / 7 , b ) 5 / 7 , c ) 4 / 7 , d ) 3 / 7 , e ) 2 / 7
Output: c
Problem: the probability that a number selected at random from the first 50 natural numbers is a composite number is ? 
Options: a ) 17 / 65 , b ) 17 / 25 , c ) 17 / 28 , d ) 17 / 65 , e ) 17 / 39
Output: b
Problem: a certain club has 10 members , including parry . one of the 10 members is chosen at random to be the president , one of the remaining 9 members is to be chosen at random to be the secretary , and one of the remaining 8 members is to be chosen at random to be the treasurer . what is the probability that parry will be either the member chose to be secretary or the member chose to be treasurer ? 
Options: a ) 1 / 720 , b ) 1 / 80 , c ) 1 / 10 , d ) 1 / 9 , e ) 1 / 5
Output: e
Problem: three 6 faced dice are thrown together . the probability that all the three show the same number on them is - 
Options: a ) 1 / 39 , b ) 1 / 36 , c ) 1 / 32 , d ) 1 / 31 , e ) 1 / 30
Output: b
Problem: a bag contains 6 black and 8 white balls . one ball is drawn at random . what is the probability that the ball drawn is white ? 
Options: a ) 3 / 4 , b ) 4 / 7 , c ) 1 / 7 , d ) 1 / 8 , e ) 4 / 3
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 w 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: from a pack of 52 cards , two cards are drawn together at random . what is the probability of both the cards being kings ? 
Options: a ) 1 / 15 , b ) 25 / 57 , c ) 35 / 256 , d ) 1 / 221 , e ) 2 / 15
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 9 managers , if 3 managers will not attend the meeting together . 
Options: a ) 1.24 , b ) 2.91 , c ) 3.12 , d ) 4.126 , e ) 5.15
Output: a
Problem: what is the probability that a number selected from number 1 to 30 is prime number , when each of the given numbers is equally likely to be selected ? 
Options: a ) 10 / 30 , b ) 20 / 30 , c ) 1 , d ) 5 / 30 , e ) 15 / 30
Output: a