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

  • question_answer
    If A and B are two events such that \[P\,(A)=\frac{1}{3}\], \[P\,(B)=\frac{1}{4}\]  and \[P\,(A\cap B)=\frac{1}{5},\] then \[P\,\left( \frac{{\bar{B}}}{{\bar{A}}} \right)=\]

    A)                 \[\frac{37}{40}\]  

    B)                 \[\frac{37}{45}\]

    C)                 \[\frac{23}{40}\]  

    D)                 None of these

    Correct Answer: A

    Solution :

                    \[P\left( \frac{{\bar{B}}}{{\bar{A}}} \right)=\frac{1-P(A\cup B)}{P(\bar{A})}=\frac{1-\frac{23}{60}}{1-\frac{1}{3}}=\frac{37}{60}\times \frac{3}{2}=\frac{37}{40}.\]


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