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VIT Engineering VIT Engineering Solved Paper-2015

  • question_answer
    If A, B, C are three events associated with a random experiment, then\[P\left( A \right)P\left( \frac{B}{A} \right)P\left( \frac{C}{A}\cap B \right)\] is

    A) \[P\left( A\cup B\cup C \right)\]              

    B) \[P\left( A\cap B\cap C \right)\]

    C) \[P\left( \frac{C}{A}\cap B \right)\]                         

    D) \[P\left( \frac{B}{A} \right)\]

    Correct Answer: B

    Solution :

    \[p\left( A \right)p\left( \frac{B}{A} \right)p\left( \frac{C}{A}\cap B \right)\]                    \[=p\left( A\cap B \right)p\left( \frac{C}{A}\cap B \right)\]                    \[=\frac{p\left( A\cap B \right)p\left[ C\cap \left( A\cap B \right) \right]}{p\left( A\cap B \right)}\]                    \[=p\left( A\cap B\cap C \right)\]


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