A student appears for tests I, II and III. The student is successful if he passes in tests I, II or I, III. The probabilities of the student passing in tests I, II and III are respectively p, q and 1/2. If the probability of the student to be successful is 1/2. Then

The probability that a non-leap year selected at random will have 53 Sunday is

Let A and B be two events such that P(A $$ \cap $$ B) = $${1 \over 6}$$, P(A $$\cup$$ B) = $${31 \over 45}$$ and P($$\overline B $$) = $${7 \over 10}$$, then

In a group of 14 males and 6 females. 8 and 3 of the males and females, respectively are aged above 40 yr. The probability that a person selected at random from the group is aged above 40 yr given that the selected person is a female, is