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

  • question_answer
    If the probability of X to fail in the examination is 0.3 and that for Y is 0.2, then the probability that either X or Y fail in the examination is                                                [IIT 1989]

    A)                 0.5         

    B)                 0.44

    C)                 0.6         

    D)                 None of these

    Correct Answer: B

    Solution :

                       Here                                                                                              \[P(X)=0.3;\]                                                                                                \[P(Y)=0.2\]                    Now                                                                         \[P(X\cup Y)=P(X)+P(Y)-P(X\cap Y)\]                    Since these are independent events, so                                                                                                                                                                  \[P(X\cap Y)=P(X)\,.\,P(Y)\]                                 Thus required probability                                                                                   \[=0.3+0.2-0.06=0.44\] .


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