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

Solution:
Here, Sample space `S={G,G},{G,B},{B,G},{B,B}`
.(i) for both being girls=A; for youngest being girl=B,so, `P(frac{A}{B})=frac{P(AnnB)}{P(B)}=frac{frac{1}{4}}{frac{2}{4}}=frac{1}{2}`
;(ii)both are girls=A,atleast one is a girl=B,so,`P(frac{A}{B})=frac{P(AnnB)}{P(B)}=frac{frac{1}{4}}{frac{3}{4}}=frac{3}{4}`