Question

A man and a woman appear in an interview for two vacanciesin the same post the probability of a mans selection is 1/4

Answer 1

Yes, they are independent events.

One way of reaching this conclusion is by using the condition for 2 independent events A and B: P(A) * P(B) = P(A intersection B)

here,

1/4 * 1/3 = 1/12 = P(man and woman both employed)

You can also look at this logically. Since there r 2 vacancies, the man and the woman are not competing. So their chances of getting hired is independent of each other.