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

Question

Assume that each born child is equally likely to be a boy or a girl. If two families have two children each,
then the conditional probability that all children are girls given that at least two are girls is :

Accepted Answer

A = At least two girls

B =  All girls

$$P\left( {{B \over A}} \right) = {{P\left( {B \cap A} \right)} \over {P\left( A \right)}}$$

$$ \Rightarrow {{P(B)} \over {P(A)}} = {{{{\left( {{1 \over 4}} \right)}^2}} \over {1 - {}^4{C_0}{{\left( {{1 \over 2}} \right)}^4} - {}^4{C_1}{{\left( {{1 \over 2}} \right)}^4}}}$$

$$ \Rightarrow {1 \over {16 - 1 - 4}} = {1 \over {11}}$$

Solutions · 1