Assume that each child born 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?

Explanation

Let Sample `S={{GG}, {GB}, {BG}, {BB}}`


(i) A= shows Both girls


B= shows Youngest is a girl

`
P(frac{A}{B})=frac{P(A cap B)}{P(B)}=frac{overline{4}}{frac{1}{4}}=frac{1}{2}`


(ii) A: shows Both girls


B: shows atleast one is a girl

`
.P(frac{A}{B})=frac{P(A cap B)}{P(B)})=frac{frac{1}{4}}{frac{3}{4}}=frac{1}{3}`