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

Options

A. `1/2`
B. `1/3`
C. `2/3`
D. `4/7`

Answer

D

Explanation

Here, S={(B,B,G),(G,G,G),(B,G,G),(G,B,G),(G,G,B),(G,B,B),(B,G,B),(B,B,G)}
`E_(1)`=Event tht a family has atleast one girl, then
`E_(1)`={(G,B,B),(B,G,B),(B,B,G),(G,G,B),(B,G,G),(G,B,G),(G,G,G)}
`E_(2)`=Event that the eldest child is a girl, then
`E_(2)`={(G,B,B),(G,G,B),(G,B,G,),(G,G,G)}
`thereforeE_(1)capE_(2)`={(G,B,B),(G,G,B),(G,B,G),(G,G,G)}
`thereforeP(E_(2)//E_(1))=(P(E_(1)capE_(2)))/(P(E_(1)))=(4//8)/(7//8)=4/7`