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

  • question_answer
    The probabilities that A and B will die within a year are p and q respectively, then the probability that only one of them will be alive at the end of the year is [CEE 1993; Pb. CET 2004]

    A)                 \[p+q\]  

    B)                 \[p+q-2qp\]

    C)                 \[p+q-pq\]            

    D)                 \[p+q+pq\]

    Correct Answer: B

    Solution :

                       Required probability is                    P[(A will die and \[B\] alive) or (B will die and \[A\] alive)]                    \[=P[(A\cap {B}')\cup (B\cap {A}')]\]                    Since events are independent, so                    Required probability\[=P(A)\,.\,P({B}')+P(B)\,.\,P({A}')\]                                                                      \[=p\,.\,(1-q)+q(1-p)=p+q-2pq.\]


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