JEE Main & Advanced Sample Paper JEE Main Sample Paper-5

  • question_answer
    If two events A and B are such that P (A') = 0.3, P  = 0.4, and P \[(A\cap B')\] = 0.5. then \[P\left( \frac{B}{A\cup B'} \right)\]equals

    A)  \[\frac{1}{4}\]                                  

    B)  \[\frac{1}{2}\]

    C)  \[\frac{1}{8}\]                                  

    D)  \[\frac{1}{16}\]

    Correct Answer: A

    Solution :

     It is given that \[P(\bar{A})=0.3\] and P=0.4 and \[P(A\cap B')=0.5\] where,     \[P(A)=1-P(\bar{A})=0.7\]                 \[P(A\cap \bar{B})=P(A)-P(A\cap B)=0.5\] \[\therefore \]  \[P(A\cap B)=0.5-0.3=0.2\]                 \[P(B/A\cup \bar{B})=\frac{P(B\cap (A\cup B'))}{P(A\cup \bar{B})}\]                 \[=\frac{P(A\cap B)}{1-P(B)+P(A\cap B)}\] \[=\frac{0.2}{1-0.4+0.2}=\frac{1}{4}\]

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