Question

Assume that each born child is equally likely to be a boy or a girl. If a family has two children, what is the conditional probability that both are girls given that (i) the youngest is a girl? (ii) atleast one is a girl? 

Answer 1

A family has 2 children, then Sample space = S = {BB, BG,GB,GG}, where B stands for Boy and G for Girl. 

(i) Let A and B be two event such that 

A = Both are girls = {GG} 

B = the youngest is a girl = {BG, GG}

Now, P(A/B) = (P(A ∩ B))/P(B) = (1/4)/(2/4) = 1/2

(ii) Let C be event such that 

C = at least one is a girl = {BG,GB,GG}

Now, P(A/C) = (P(A ∩ C))/P(C) = (1/4)/(3/4) = 1/3