JEE Main & Advanced AIEEE Paper (Held On 11 May 2011)

  • question_answer
    Let A, B, C be pariwise independent events with P > 0 and \[P(A\cap B\cap C)=0.\] Then \[P({{A}^{c}}\cap {{B}^{c}}/C).\]     AIEEE  Solved  Paper (Held On 11 May  2011)

    A) \[P(1)-P({{B}^{c}})\]

    B) \[P({{A}^{c}})+P({{B}^{c}})\]

    C) \[P({{A}^{c}})-P({{B}^{c}})\]

    D) \[P({{A}^{c}})-P(B)\]

    Correct Answer: D

    Solution :

                    \[P({{A}^{c}}\cap {{B}^{c}}/C)=\frac{P(({{A}^{c}}\cap {{B}^{c}})\cap C)}{P(C)}\] \[=\frac{P(C)-P(A\cap C)-P(B\cap C)+P(A\cap B\cap C)}{P(C)}\] \[=\frac{P(C)-P(A).P(C)-P(B)P(C)+0}{P(C)}\] \[=1-P(A)-P(B)\] \[=P({{A}^{c}})-P(B)\]

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