Assume that in a family, each child is equally likely to be a boy or girls. A family with three children is is chosen at random. The probability that the eldest child is a girls given that the family has at least one girls is.

Explanation

Total sample space `S={(B,B,B), (G,G,G), (B,G,G), (G,B,G), (G,G,B), (G,B,B), (B,G,B), (B,B,G)}=8`



`E_1=` At least one girl


`E_1={(G,B,B), (B,G,B), (B,B,G), (G,G,B), (B,G,G), (G,B,G), (G,G,G)}=7/8`


`E_2=` Eldest girl child


`E_2={(G,B,B), (G,G,B), (G,B,G), (G,G,G)}=4/8`



Intersection of two events:


`E_1nnE_2={(G,B,B), (G,G,B), (G,B,G), (G,G,G)}=4/8`


`P(E_2//E_1)=(P(E_1nnE_2))/(P(E_1))=(4/8)/(7/8)=4/7`