Question

Assume that each born child is equally likely to be a boy or a girl. If two families have two children each, if conditional probability that all children are girls given that at least two are girls is $k$, then $\frac{1}{k} =$

Answer 1

Let, $A = $ At least two girls
$B =$ All girls
$P(\frac{B}{A}) = \frac{P(B \cap A)}{P(A)} = \frac{P(B)}{P(A)}$
$ = \frac{(\frac{1}{4})^4}{1 -\,{}^4C_0 (\frac{1}{2})^4 - \,{}^4C_1(\frac{1}{2})^4}$
$ = \frac{1}{16 - 1 - 4} = \frac{1}{11}$