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JEE Main & Advanced Mathematics Probability Question Bank Conditional probability bayes theorem

  • question_answer
    A pair has two children. If one of them is boy, then the probability that other is also a boy, is

    A)                 \[\frac{1}{2}\]       

    B)                 \[\frac{1}{4}\]

    C)                 \[\frac{1}{3}\]       

    D)                 None of these

    Correct Answer: C

    Solution :

                      Let \[P(A)=\] probability of a boy in two children \[=\frac{3}{4}\]            Because cases are \[BB,\,BG,\,GB,\,GG=4\]            Favourable cases are \[BB,\,BG,\,GB=3\]            The probability that the second child is also boy is            \[P(A\cap B)=\frac{1}{4}\]                 We have to find \[P(B/A)=\frac{P(A\cap B)}{P(A)}=\frac{1/4}{3/4}=\frac{1}{3}.\]


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