CAT Question Bank  Probability

Number of Questions  30
Topic  Probability
Answer key available?  No
Source  Curated Content

Q1) Three biased coins A, B and C are such that the probability of getting a head when A is tossed is 1/4, the probability of getting a head when B is tossed is 3/4 and the probability of getting a head when C is tossed is 2/3. The three coins are tossed. If it is found that there are two heads and one tail, what is the probability that coin A shows a head?

Q2) In a match India vs SA, the odd against India winning the match is 2:1. What is the probability that India would win a three match series against SA if there is no possibility of draw in a match?

Q3) A stick is broken into three pieces. Find the probability a triangle can be formed with the pieces.

Q4) Find the probability that a leap year selected at random will contain 53 Sundays ?

Q5) 5 persons entered the lift cabin on the ground floor house of an 8 floor house .Suppose that each of them independently and with equal probability can leave the cabin at any floor beginning with the first , then the probability of all 5 persons leaving at different floor is?

Q6) Certain numbers of children were playing a game of football. There was a trial taking place on the field. In this trial the probability that a goal is scored is 2/5. The probability that a girl hits a goal is 7/10 whereas the probability that a boy hits a goal is 1/5. What will be the probability that not only a goal is hit girl but it is also hit by a boy?

Q7) There are two boxes, one containing 10 red balls and the other containing 10 green balls. You are allowed to move the balls between the boxes so that when you choose a box at random and a ball at random from the chosen box, the probability of getting a red is maximized. This maximum probability is
a) 37/38
b) 1/2
c) 14/19
d) 3/4

Q8) A and B write an exam. The probability that A fails is 0.2. The probability that both A and B fail together is 0.15. The probability that B fails alone is 0.15. The event “A fails alone” implies that A fails when B passes the exam and vice versa. The probability that A fails when B has failed is

Q9) You have three bags, each containing two marbles. Bag A contains two white marbles, Bag B contains two black marbles, and Bag C contains one white marble and one black marble. You pick a random bag and take out one marble. It is a white marble. What is the probability that the remaining marble from the same bag is also white?

Q10) The Johnson Company receives connector rods from three different producers. We will call them Company A, Company B and Company C. As the quality control inspector you check the rods as they come in. From past experience you know that 12% of the rods from Company A are faulty, 8% of the rods from Company B are faulty and 9% of the rods from Company C are faulty. 40% of the rods come from Company A, 30% come from Company B and 30% come from Company C. You randomly pick a connector rod and find out that it is faulty. What is the probability that it came from Company C?

Q11) Three points p, q and r are selected at random from the circumference of a circle. Find the probability that the points lie on a semicircle.

Q12) Two aeroplanes bomb the target in succession. The probability of A & B hitting correctly are 0.7 & 0.2 respectively. The second plane shall bomb only if the first misses the target. Find the probability that the target is hit by the second plane.

Q13) Aditya has a total of 18 Red and blue balls in 2 bags (each bag having balls of both colors). A ball is drawn at random from 1st bag followed by drawing another ball from 2nd bag, the probability of both being red is 5/16. what is the probability of both being blue

Q14) You tossed three unbiased coins then remove all tails in the result, and you tossed the remaining coins. What is the probability that you tossed exactly three tails in the remaining coins?

Q15) After the typist writes 12 letters and addresses 12 envelopes, she inserts the letters randomly into the envelopes (1letter per envelope). What is the probability that exactly 1 letter is inserted in an improper envelope?

Q16) Three numbers are to be selected at random without replacement from set of numbers (1,2,3,........n). The conditional probability that the third number lies between the first two, if the first number is known to be smaller than the second?

Q17) An urn contains 5 red, 1 black, few white and few blue balls.The probability of picking out 1 white ball is 1/5 and probability of picking out 1 blue ball is 1/2. When three balls are picked at random, what is the probability that none of them is blue?

Q18) Given that the product of the digits of a 4 digit number abcd with distinct nonzero digits is a multiple of 3, what is the probability that the product will also be a multiple of 9 ?

Q19) If 3 consecutive letters are selected at random from the English alphabet, then the probability that all three are consonants is:
a) 1/2
b) 11/24
c) 5/12
d) 7/12