Probability and Combinatorics is important topic for CAT. The questions asked from this topic are significantly high. The chances of occurring or not occurring an event should be determined based on the number of favorable and not favorable conditions. Here we are giving some important probability questions from CAT previous papers. The candidates are advised to try each questions on their own and later go through the solutions given below.

**CAT Probability Questions With Solutions:**

Download Probability Questions Set-2 PDF

**Question 1:
**

For a scholarship, at most n candidates out of 2n + I can be selected. If the number of different ways of selection of at least one candidate is 63, the maximum number of candidates that can be selected for the scholarship is:

**A.Â **3

**B.**Â 4

**C.Â **2

**D.Â **5

Probability Questions for CAT SET-1

**Question 2:**

In how many ways can eight directors, the vice chairman and chairman of a firm be seated at a round table, if the chairman has to sit between the the vice chairman and a specific director?

**
A.Â **9! x 2

**Â 2 x 8!**

B.

B.

**2 x 7!**

C.Â

C.Â

**None of these**

D.Â

D.Â

**Question 3:**

A player rolls a die and receives the same number of rupees as the number of dots on the face that turns up. What should the player pay for each roll if he wants to make a profit of one rupee per throw of the die in the long run?

**A.Â **Rs. 2.50

**B.Â **Rs. 2

**C.Â **Rs. 3.50

**D.Â **Rs. 4

**Question 4:
**

In how many ways is it possible to choose a white square and a black square on a chessboard so that the squares must not lie in the same row or column?

**A.**Â 56

**B.**Â 896

**C.**Â 60

**D.**Â 768

**Question 5:**

A man has 9 friends: 4 boys and 5 girls. In how many ways can he invite them, if there has to be exactly 3 girls in the invitees?

**
A.Â **320

**B.Â **160

**C.Â **80

**D.Â **200

IIFT PREVIOUS PAPERS WITH SOLUTIONS

**Solutions:**

**1)**Â Answer (C)

At least one candidate and atmost n candidates among 2n+1 candidates => $^{2n+1}C_1$ +Â $^{2n+1}C_2$ + …Â $^{2n+1}C_{n-1}$ +Â $^{2n+1}C_n$

=>Â $^{2n+1}C_1$ +Â $^{2n+1}C_2$ + …Â $^{2n+1}C_{n-1}$ +Â $^{2n+1}C_n$ = 63

n = 3 satisfies this equation.

Hence, at most 3 candidates can be selected for scholarship.

**2)**Â Answer (C)

Chariman, Vice-Chairman and the director can be made as a

group such that Chairman sits between the Vice-Chairman

and the director. This group can be formed in 2 ways.

Each of the remaining 7 directors and the group can be

arranged in 7! ways.

=> Total number of ways = 2 * 7!.

**3)**Â Answer (A)

The expected money got by the player = 1*1/6 + 2*1/6 +

3*1/6 + 4*1/6 + 5*1/6 + 6*1/6 = 21/6 = Rs 3.5

So, the player has to pay 3.5 – 1 = Rs 2.5 to get a profit of Re

1 in the long run.

XAT Previous Papers with Solutions

**4)**Â Answer (D)

First a black square can be selected in 32 ways. Out of

remaining rows and columns, 24 white squares remain. 1

white square can them be chosen in 24 ways. So total no. of

ways of selection is 32*24 = 768.

**5)** Answer (B)

Selecting 3 girls from 5 girls can be done in $^5C_3$ ways => 10 ways

Each of the boys may or may not be selected => 2 * 2 * 2 * 2 = 16 ways

=> 16 * 10 = 160 ways.

Hope you find this CAT probability questions and answers useful for the exam. Also go through all the Quantitative Aptitude for CAT Questions.