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JEE Main & Advanced Mathematics Probability Question Bank Self Evaluation Test - Probability-II

  • 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) \[P\overline{\left( \frac{A}{b} \right)}=\frac{3}{4}\]

    D) None of these

    Correct Answer: C

    Solution :

    [c] 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, \[P\left( \frac{A}{B} \right)=\frac{1}{4}\Rightarrow P\overline{\left( \frac{A}{B} \right)}=1-\frac{1}{4}=\frac{3}{4}.\]


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