Question : A father has 3 children with at least one boy. The probability that he has 2 boys and 1 girl is
(A) 1/4
(B) 1/3
(C) 2/3
(D) none of these
Answer : option (B)
Solution :
Consider the following events:
A: Father has at least one boy
B: father has 2 boys and one girl
Then, A = one boy and 2 girls, 2 boys and one girl, 3 boys and no girl
AnB = 2 boys and one girl
Now, the required probability is
P(A/B) = P(AnB)/P(B)
=1/3