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

  • question_answer
    If \[P(A)=P(B)=x\] and \[P(A\cap B)=P({A}'\cap {B}')=\frac{1}{3}\], then \[x=\] [UPSEAT 2003]

    A)                 \[\frac{1}{2}\]       

    B)                 \[\frac{1}{3}\]

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

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

    Correct Answer: A

    Solution :

                       \[P(A'\cap B')=1-P(A\cup B)\Rightarrow \,P(A\cup \,B)=\frac{2}{3}\]                    Now \[P(A\cup B)\,=P(A)+P(B)-P(A\cap B)\]                                 Þ \[\frac{2}{3}=x+x-\frac{1}{3}\Rightarrow \,x=\frac{1}{2}\].


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