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JEE Main & Advanced Sample Paper JEE Main Sample Paper-28

  • question_answer
    If two events A and B are such that \[P(A')=03\], \[P(B)=0.4\] and \[P(A\cap B')=0.5\], then \[P\left( \frac{B}{A\cup B'} \right)\] equals

    A)  \[\frac{3}{4}\]                                  

    B)  \[\frac{5}{6}\]

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

    D)  \[\frac{3}{7}\]

    Correct Answer: C

    Solution :

    \[P(A)=1-0.3=0.7\] \[P(B)=0.4\] \[P(A\cap \overline{B})=0.5\Rightarrow P(A)-P(A\cap B)=0.5\] \[\Rightarrow \]\[P(A\cap B)=0.2\] Now, \[P\left( \frac{B}{A\cup \overline{B}} \right)=\frac{P(B\cap (A\cup \overline{B}))}{P(A\cup \overline{B})}\] \[=\frac{P\left( (B\cap A)\cup (B\cap \overline{B}) \right)}{P(A)+P(\overline{B})-P(A\cap \overline{B})}\] \[=\frac{P(B\cap A)}{P(A)+P(\overline{B})-P(A\cap \overline{B})}=\frac{0.2}{0.8}=\frac{1}{4}\]


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