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

  • question_answer
    If \[P(A)=\frac{1}{2},\,\,P(B)=\frac{1}{3}\] and \[P(A\cap B)=\frac{7}{12},\] then the value of \[P\,({A}'\cap {B}')\] is

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

    B)                 \[\frac{3}{4}\]

    C)                 \[\frac{1}{4}\]       

    D)                 \[\frac{1}{6}\]

    Correct Answer: B

    Solution :

                       \[P({A}'\cap {B}')=1-P(A\cup B)\]                                                 \[=1-\left( \frac{1}{2}+\frac{1}{3}-\frac{7}{12} \right)=1-\frac{1}{4}=\frac{3}{4}\].


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