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Question

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?

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Solution

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}EF=(gg)=En(F)=3,(EF)=1Required probability=P(EF)=P(EF)P(F)=P(E)P(F)=1434=13


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