A man and his wife appear in an interview for two vacancies in the same post. The probability of the husband's selection is (1/7) and the probability of the wife's selection is (1/5). What is the probability that only one of them is selected?
Let A = Event that the husband is selected
and B = Event that the wife is selected.
Then, `P A=1/7and P(B)=1/5`
∴ `P(barA)= (1-1/7)=6/7 and P(barB)= (1-1/5)=4/5`
∴ Required probability = P [(A and not B) or (B and not A)]
= `P[(Aand barB)or(B andbarA)]`
= `P(Aand barB)+P(B andbarA)`