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

  • question_answer
    A, B, C are any three events. If P (S) denotes the probability of S happening  then \[P\,(A\cap (B\cup C))=\] [EAMCET 1994]

    A)                 \[P(A)+P(B)+P(C)-P(A\cap B)-P(A\cap C)\]

    B)                 \[P(A)+P(B)+P(C)-P(B)\,P(C)\]

    C)                 \[P(A\cap B)+P(A\cap C)-P(A\cap B\cap C)\]

    D)                 None of these

    Correct Answer: C

    Solution :

                       \[P[A\cap (B\cup C)]=P[(A\cap B)\cup (A\cap C)]\]                                 \[=P(A\cap B)+P(A\cap C)-P[(A\cap B)\cap (A\cap C)]\]                                                 \[=P(A\cap B)+P(A\cap C)-P(A\cap B\cap C)\].


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