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

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$\frac{1}{17}$

$\frac{1}{12}$

$\frac{1}{10}$

$\frac{1}{11}$

answer is A.

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Detailed Solution

$A =$ At least two girls
$B =$ All girls
$P (\frac{B}{A}) = \frac{P (B \cap A)}{P (A)} = \frac{P (B)}{P (A)} = \frac{{(\frac{1}{2})}^{4}}{1 -^{4} C_{0} {(\frac{1}{2})}^{4} -^{4} C_{1} {(\frac{1}{2})}^{4}} = \frac{1}{16 - 1 - 4} = \frac{1}{11}$

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