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JEE Main & Advanced Mathematics Probability Question Bank Odds in favour and odds against Addition theorem on probability

  • question_answer
    If A and B an two events such that \[P\,(A\cup B)=\frac{5}{6}\],\[P\,(A\cap B)=\frac{1}{3}\] and \[P\,(\bar{B})=\frac{1}{3},\] then \[P\,(A)=\]

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

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

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

    D)                 \[\frac{2}{3}\]

    Correct Answer: C

    Solution :

                       \[P(A)=P(A\cap B)+P(A\cup B)-P(B)\]                                         \[=\frac{1}{3}+\frac{5}{6}-\frac{2}{3}=\frac{3}{6}=\frac{1}{2}.\]


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