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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 \[P\,(A)\ne 0\] and \[P\,(B)\ne 1,\] then \[P\,\left( \frac{{\bar{A}}}{{\bar{B}}} \right)=\] [IIT 1982; RPET 1995, 2000; DCE 2000; UPSEAT 2001]

    A)                 \[1-P\,\left( \frac{A}{B} \right)\]           

    B)                 \[1-P\,\left( \frac{{\bar{A}}}{B} \right)\]

    C)                 \[\frac{1-P\,(A\cup B)}{P\,(\bar{B})}\]               

    D)                 \[\frac{P\,(\bar{A})}{P\,(\bar{B})}\]

    Correct Answer: C

    Solution :

                    \[P\left( \frac{\overline{A}}{\overline{B}} \right)=\frac{P(\overline{A}\cap \overline{B})}{P(\bar{B})}=\frac{P(\overline{A\cup B})}{P(\bar{B})}=\frac{1-P(A\cup B)}{P(\bar{B})}.\]


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