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11th Class Mathematics Sample Paper Mathematics Olympiad - Sample Paper-7

  • question_answer
    If A and B are two independent events such that \[\mathbf{P}\left( A \right)>\mathbf{0}\]and \[P(B)\ne 1\], then \[P\left( \frac{\overline{A}}{\overline{B}} \right)\]. is     to:

    A)  \[\frac{P(\overline{A})}{P(\overline{B})}\]                      

    B)  \[\frac{1-P(A\cup B)}{P(B)}\]

    C)  \[1-P\left( \frac{A}{B} \right)\]               

    D)  \[1-P\left( \frac{A}{\overline{B}} \right)\]

    Correct Answer: B

    Solution :

    [b] \[\because P\left( \frac{\overline{A}}{\overline{B}} \right)=\frac{1-P(\overline{A}\cap \overline{B})}{P(\overline{B})}\] \[=\frac{P\left( \overline{A\cup B} \right)}{P\left( \overline{B} \right)}=\frac{1-P\left( A\cup B \right)}{P(\overline{B})}\]             Hence option [b] is correct.


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