• # question_answer 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 : [JEE Main 10-4-2019 Morning] A) $\frac{1}{11}$           B) $\frac{1}{17}$ C) $\frac{1}{10}$                                   D) $\frac{1}{12}$

$P\left( B \right)=P\left( G \right)=1/2$ Required Proballity = $\frac{\text{all 4girls}}{\left( \text{all 4girls} \right)\text{ (exactly+3girls+1boy)+(exactly2girls+2boys)}}$            $=\frac{{{\left( \frac{1}{2} \right)}^{4}}}{{{\left( \frac{1}{2} \right)}^{4}}{{+}^{4}}{{C}_{3}}{{\left( \frac{1}{2} \right)}^{4}}{{+}^{4}}{{C}_{2}}{{\left( \frac{1}{2} \right)}^{4}}}=\frac{1}{11}$