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) at least one is a girl.

Answer 1

Sample space $S=\{GG,GB,BG,BB\}$
(i) A = Both are girls
B = Youngest is a girl
$P\left(\frac{A}{B}\right)=\frac{P(A\cap B)}{P\left(B\right)}=\frac{\frac{1}{4}}{\frac{2}{4}}=\frac{1}{2}$
(ii) A: Both are girls
B: atleast one is a girl
$P\left(\frac{A}{B}\right)=\frac{P(A\cap B)}{P\left(B\right)})=\frac{\frac{1}{4}}{\frac{3}{4}}=\frac{1}{3}$