JEE Main & Advanced JEE Main Paper (Held on 10-4-2019 Morning)

  • 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) \[\frac{1}{12}\]

    Correct Answer: A

    Solution :

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

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