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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


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`

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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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