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

Sample space `S={G G, G B, B G, B B}`

(i) `A=` Both are girls

`B=` Youngest is a girl

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

(ii) A: Both are girls

B: atleast one is a girl

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