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

  • question_answer
    \[P(A\cup B)=P(A\cap B)\]if and only if the relation between \[P(A)\] and \[P(B)\] is                                    [IIT 1985]

    A)                 \[P(A)=P(\bar{A})\]             

    B)                 \[P\,(A\cap B)=P(A'\cap B')\]

    C)                 \[P\,(A)=P\,(B)\]    

    D)                 None of these

    Correct Answer: C

    Solution :

                       \[P(A)=P(B)\]                    As this gives \[P(A\cup B)=P(A)+P(B)-P(A\cap B)\]                                 or \[P(A)=2P(A)-P(A)\]\[\Rightarrow P(A\cup B)=P(A\cap B).\]


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