Question

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?

पर्याय

• `2/7`

• `1/7`

• `3/4`

• `4/5`

Answer 1

`2/7`

Explanation:
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)`

= `P(A).P(barB)+P(B).(barA)`

= `(1/7xx4/5)+(1/5xx6/7)`

= `10/35=2/7`