Q. 9. Two dice are thrown. Find the probability that sum of the numbers on two dice is 9, given that the first die shows 6. (Dec. 2001)

Solution. Two dice can be thrown in 6 X 6 = 36 ways.
A total of 9 can be obtained as
(6, 3), (3, 6), (5, 4), (4, 5), i.e., in 4 ways.

Required probability = 4/36 or 1/9.

Q. 10. The probability of a college student being male is 1/3 and that of being female is 2/3. The probability that a male student completes the course is 5/14 and that of a female student completes is 5/11. A student is selected at random and is found to have completed the course. What is the probability that the student is a male? (June 2000)

Solution. This problem is based on Bayes theorem.
Let A = an event that the student completes the course
B₁ = an event that the student selected is male
B₂ = an event that the student selected is female

Therefore, P(B₁) = 1/3, P(B₂) = 2/3
P(A | B₁) = 5/14, P(A | B₂) = 5/11

or P(B₁ | A) = 0.28
Thus, the probability that the student being male is 0.28.