Let A = Event that the brother is selected and B = Event that the wife is selected Then, P(A)=
1
8
and P(B)=45 ∴ P(A)=1−P(A) =1−
1
8
=
7
8
and P(B)=1−P(B) =1−
4
5
=
1
5
Required probability = Probability that only one of them is selected = P[(A and not B) or (B and not A)] = P (A and B) or ( B and A ) = P(A and B ) P(B and A ) =P(A).P(B)+P(B).P(A) =