13.12   Assume that each born child 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,

Answers (1)

   Assume that each born child is equally likely to be a boy or a girl.

  Let  first and second girl are denoted by G1\, \, \, and \, \, \,G2  respectively also  first and second boy are denoted by B1\, \, \, and \, \, \,B2

   If a family has two children, then total outcomes =2^{2}=4=\left \{ (B1B2),(G1G2),(G1B2),(G2B1)\right \}

   Let A= both are girls =\left \{(G1G2)\right \} 

   and  B= the youngest is a girl ==\left \{(G1G2),(B1G2)\right \}

A\cap B=\left \{(G1G2)\right \}

P(A\cap B)=\frac{1}{4}              P( B)=\frac{2}{4}

P(A| B)=\frac{P(A\cap B)}{P(B)}

P(A| B)=\frac{\frac{1}{4}}{\frac{2}{4}}

P(A| B)=\frac{1}{2}

Therefore, the required probability is 1/2

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