Probability Questions

Probability is one of the important topics of CAT examination, probability questions test both Mathematical and Reasoning skill of a candidate, here we are providing some questions which will help candidates to prepare for the examination.


Test Your Probability Skills – Questions

1)What is the probability of forming the word “ADDS” by picking 4 cards at random and kept in the same order out of 50 cards given with 10 cards having “A”, 10 having “S” and the remaining 30 having “D” on it?

(a) 22/54

(b) 15/[(48-1)(48+1)x4]

(c) 1/502 (d) 10/47

(d) 10/47


2) A table is set up which can seat 5 people from 4 Adults and 6 children. Find the probability that the table seats at least 2 children?

(a) 31/42

(b) 124/126

(c) 41/42

(d) 3/26


3) For a drama, 3 students need to be selected out of 6 students A, B, C, D, E and F. If A is already selected, what is the probability of selecting C also?

(a) 0.5

(b) 0.2

(c) 0.3

(d) 0.4


4) If 30% of the visitors to an ice cream shop had chocolate ice-cream, then what is the probability that 2 out of 3 people who entered the store on Saturday at 5 pm will have chocolate ice cream?

(a) 0.16

(b) 0.15

(c) 0.19

(d) 0.28


5) A Number is selected at random from first thirty natural numbers. What is the chance that it is a multiple of either 3 or 13?

(a) 17/30

(b) 2/5

(c) 11/30

(d) 4/15


6) What is the probability of getting at least one six in a single throw of three unbiased dice?

(a) 1/6

(b) 125/216

(c) 1/36

(d) 91/216


7) What is the probability that a two digit number selected at random will be a multiple of ‘3’ and not a multiple of ‘5’?

(a) 2/15

(b) 4/15

(c) 1/15

(d) 3/10


8) When two dice are thrown simultaneously, what is the probability that the sum of the two numbers that turn up is less or equal to 10?

(a) 5/6

(b) 11/12

(c) 1/6

(d) 1/12


9) 4 out of 15 apples are rotten. They are taken out one by one at random and examined. The ones which are examined are not replaced. What is the probability that the 9th one examined is the last rotten one?

(a) 4C3× 11C5/15C8×1/7C1

(b)11C5×4C4 /15C9

(c) 4C3×11C5/15C9

(d) None of these


10) There are 22 red and 22 black balls in a box. Arun picks up three balls at random. What is the probability that he has two balls of the same color?

(a)2x 22C2×11C1/44C3

(b)22C2 ×22C1/44C(3

(c) 1

(d) None of these


11) A furniture shop has six identical steel cabinets of brand A and four identical steel cabinets of brand B. Three customers buy one cabinet each. Then the probability that two or more cabinets of brand A have been sold

(a) 1/3

(b) 2/3

(c) 1/2 

(d) 3/4


12) Arpit and Rita will play one game of Rock, Paper, Scissors. In this game, each will select and show a hand sign for one of the three items. Rock beats Scissors, Scissors beat Paper, and Paper beats Rock. Assuming that both Arpit and Rita have an equal chance of choosing any one of the hand signs, what is the probability that Arpit will win?

(a) 5/6

(b) 2/3

(c) 1/2

(d) 1/3


13) Two dice are thrown simultaneously. The probability of getting an even number on both the dice is?

(a) 1/2

(b) 3/4

(c) 1/4

(d) 1/5


14) Parul and Vijay throw 3 dice in a single throw. It is known that Parul throws a total of 16. Find Vijay’s probability of getting a higher value.

(a) 1/4

(b) 1/3

(c) 1/52

(d) 1/36


15) Arun draws 3 balls at random from a basket which contains 4 red and 5 blue balls. What are the odds in favor of these being all blue?

(a) 5: 42

(b) 5: 37

(c) 4: 43

(d) 4: 50


16) 12 people, including the MD, the CFO, and 10 executives are to be seated around a circular table. Find the probability that there are at least 3 executives sitting between the MD and the CFO

(a) 5/10

(b) 3/5

(c) 1/3

(d) 5/11


17) In a single throw of 2 dice, the odds against drawing 7 are?

(a) 1: 5

(b) 2: 5

(c) 1: 6

(d) 5: 1


18) The integers p and q are chosen at random between 1 and 100, then the probability that a number of the form 7p+7q is divisible by 5 is?

(a) 1/4

(b) 1/2

(c) 1/5 

(d) 3/4


19) A wooden cask contains some tools i.e. exactly 12 nuts and 24 bolts. 1/3rd of each of these are defective. If 2 tools are picked up one after the other without replacement, then what is the probability that both are not defective?

(a) 45/106

(b) 23/135

(c) 46/105 

(d) 89/105


20) Two squares are chosen at random from the small squares drawn on a chessboard. What is the chance that the two squares chosen have exactly one corner in common?

(a) 0.052 

(b) 0.042

(c) 0.048

(d) 0.075


21) If the XAT center of 4 students can be any one of the 7 cities, then calculate the probability that all the 4 students get any one of exactly 2 centers.

(a) 3/49

(b) 6/49

(c) 7/48

(d) 12/39


22) 6 boys and 3 girls are randomly placed in a row. Determine the probability of no two girls being placed adjacently.

(a) 7/23

(b) 7/24

(c) 8/23

(d) 9/24


23) What is the probability that product of two integers chosen at random has the same unit’s digit as the integers themselves?

(a) 3/10 

(b) 1/25 

(c) 4/15 

(d) 7/15

24) A man speaks truth 3 out of 4 times. He throws a die and reports that it is a six. Find the probability that it is actually a six.

(a) 2/3

(b) 3/4 

(c) 1/8 

(d) 2/7


25) An experiment succeeds twice as often as it fails. What is the probability that in the next 5 trials there will be four successes?

(a) 82/232 

(b) 17/53

(c) 80/213 

(d) 80/243


For the detailed solution to the above questions, visit probability solutions.

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