Assume that each child born is equaly likely to be boy or a girl. IF a family has two children, what is the conditional probability that both are girls given that
atleast one is a girl?
Let B and g represent th boy and the girl child, respectively, If a family has two children, the sample space will be
S = (bb, bg, gb, gg)
Which contains four eqally likely sample points i.e. n (S) = 4
Let E : both hcildren are girls then E ={gg}⇒n(E)=1
Let F: atleast one is a girl, then F={bg,gb,gg}⇒E∩F=(gg)=E⇒n(F)=3,(E∩F)=1∴Required probability=P(EF)=P(E∩F)P(F)=P(E)P(F)=1434=13