(a) In answering a question on a multiple choice test, a student either knows the answer or guesses. Let ‌

3

5

be the probability that he knows the answer and ‌

2

5

be the probability that he guesses. Assuming that a student who guesses at the answer will be correct with probability ‌

1

3

. What is the probability that the student knows the answer, given that he answered it correctly?
OR
(b) A box contains 10 tickets, 2 of which carry a prize of ₹ 8 each, 5 of which carry a prize of ₹ 4 each, and remaining 3 carry a prize of ₹2 each. If one ticket is drawn at random, find the mean value of the prize.