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

  • question_answer
    If A and B are two independent events such that \[P\,(A\cap B')=\frac{3}{25}\] and \[P\,(A'\cap B)=\frac{8}{25},\] then \[P(A)=\] [IIT Screening]

    A)                 \[\frac{1}{5}\]       

    B)                 \[\frac{3}{8}\]

    C)                 \[\frac{2}{5}\]       

    D)                 \[\frac{4}{5}\]

    Correct Answer: A

    Solution :

                       Since events are independent.                    So, \[P(A\cap {B}')=P(A)\times P({B}')=\frac{3}{25}\]                    \[\Rightarrow P(A)\times \{1-2P(B)\}=\frac{3}{25}\]                     .....(i)                    Similarly, \[P(B)\times \{1-P(A)\}=\frac{8}{25}\]                             .....(ii)                                 On solving (i) and (ii), we get \[P(A)=\frac{1}{5}\] and \[\frac{3}{5}\].


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