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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 events such that \[P\,(A\cup B)\,+P\,(A\cap B)=\frac{7}{8}\] and \[P\,(A)=2\,P\,(B),\] then \[P\,(A)=\]

    A)                 \[\frac{7}{12}\]    

    B)                 \[\frac{7}{24}\]

    C)                 \[\frac{5}{12}\]    

    D)                 \[\frac{17}{24}\]

    Correct Answer: A

    Solution :

                       Since we have            \[P(A\cup B)+P(A\cap B)=P(A)+P(B)\]\[=P(A)+\frac{P(A)}{2}\]                                 \[\Rightarrow \frac{7}{8}=\frac{3P(A)}{2}\Rightarrow P(A)=\frac{7}{12}.\]


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