18. The probability that A speaks the truth is $\frac{4}{5}$ and that of B speaking the truth is $\frac{3}{4}$. The probability that they contradict each other in stating the same fact is :

(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.

A person has a fruit box that contains 6 apples and 4 oranges. He picks out a fruit three times, one after the other, after replacing the previous one in the box. Find: (i) The probability distribution of the number of oranges he draws. (ii) The expectation of the random variable (number of oranges).

A person is Head of two independent selection committees I and II. If the probability of making a wrong selection in committee I is 0.03 and that in committee II is 0.01, then find the probability that the person makes the correct decision of selection: (i) in both committees (ii) in only one committee.

A biased die is twice as likely to show an even number as an odd number. If such a die is thrown twice, find the probability distribution of the number of sixes. Also, find the mean of the distribution.