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 :

• A. $\frac{1}{10}$
• B. $\frac{1}{11}$
• C. $\frac{1}{12}$
• D. $\frac{1}{17}$

Answer 1

The correct option is B $\frac{1}{11}$

Probability of a girl = Probability of a boy $=\frac{1}{2}$

Required probability $=\frac{{\left(\frac{1}{2}\right)}^4}{{\left(\frac{1}{2}\right)}^4+{}^4{C}_2{\left(\frac{1}{2}\right)}^4+{}^4{C}_3{\left(\frac{1}{2}\right)}^4}$
$=\frac{1}{11}$