# 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 Prob - Mathematics

MCQ

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?

• 2/7

• 1/7

• 3/4

• 4/5

#### Solution

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

Concept: Probability (Entrance Exam)
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