CAT Probability Questions With Solutions Set-2

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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:

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

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

B.
Â 2 x 8!

C.Â
2 x 7!

D.Â
None of these

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

Solutions:

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.

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!.

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.

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