A couple has two children. Find the probability that
(i) both the children are boys, if it is known that the older child is a boy.
(ii) both the children are girls, if it is known that the older child is a girl.

Evaluate P(AUB) if 2P(A) = P(B) = \(\frac { 5 }{ 13 } \)and P(A/B) = \(\frac { 2 }{ 5 } \).

In answering a question on a multiple choice test, a student either knows the answer or guesses. Let \(\frac { 3 }{ 4 } \) be the probability that he knows the answer and \(\frac { 1 }{ 4 } \) be the probability that he guesses. Assuming that a student who guesse at the answer will be correct with probability \(\frac { 1 }{ 4 } \). What is the probability that the student knows the answer given that he answered it correctly?

A and B are two candidates seeking admission in a college. The probability that A is selected is 0.7 and the probability that exactly one of them is selected is 0.6. Find the probability that B is selected.

p(A) = 0.3, P(B) = 0.6 and \(P(A\cap B)=0.25\) .Find
(i) \(P(A\cup B)\) 
(ii) P(A/B)
(iii) \(P(B/\bar { A } )\) 
(iv) \(P(\bar { A } /B)\) 
(v) \(P(\bar { A } /\bar { B } )\)