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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2006

  • question_answer
        Let\[0<P(A)<1,0<P(B)<1\]and\[P(A\cup B)=P(A)+P(B)-P(A)\text{ }P(B),\]then

    A)  \[P(B/A)=P(B)-P(A)\]

    B)  \[P(A\cup B)=P(A)+P(B)\]

    C)  \[P(A\cap B)=P(A)P(B)\]

    D)  none of the above

    Correct Answer: D

    Solution :

                     Given\[P(A\cup B)=P(A)+P(B)-P(A).P(B)\]          ...(i) AIso \[P(A\cup B)=P(A)+P(B)-P(A\cap B)\]...(ii) From Eqs. (i) and (ii)\[P(A\cap B)=P(A)P(B)\] \[\therefore \]A and B are independent events.


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