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Manipal Engineering Manipal Engineering Solved Paper-2010

  • question_answer
    For two events A and B, it is given that\[P(A)=P\left( \frac{A}{B} \right)=\frac{1}{4}\]and\[P\left( \frac{B}{A} \right)=\frac{1}{2}\]. Then

    A)  A and B are mutually exclusive events

    B)  A and B are dependent events

    C) \[P\left( \frac{A}{B} \right)=\frac{3}{4}\]

    D)  None of the above

    Correct Answer: C

    Solution :

    We have,\[P(A)=P\left( \frac{A}{B} \right)=\frac{1}{4}\].This shows that\[A\]and\[B\]are independent events. So,                 \[P(B)=P\left( \frac{B}{A} \right)=\frac{1}{2}\] Now,     \[P\left( \frac{A}{B} \right)=\frac{1}{4}\Rightarrow P\left( \frac{{\bar{A}}}{B} \right)=1-\frac{1}{4}=\frac{3}{4}\]


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