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

  • question_answer
    For two mutually exclusive events A and B, \[P(A)=0.2\] and \[P(\bar{A}\bigcap B)=0.3.\] What is \[P(A|(A\bigcup B))\] equal to?

    A) \[\frac{1}{2}\]

    B) \[\frac{2}{5}\]

    C) \[\frac{2}{7}\]

    D) \[\frac{2}{3}\]

    Correct Answer: B

    Solution :

    [b] Event A and B are mutually exclusive. Hence \[P(A\cap B)=\phi =0\] \[\therefore \,\,\,\,P(A\cup B)=P(A)+P(B)\]             ? (1) \[P(A)=0.2\]                   [Given] \[P(B)=P(\bar{A}\cap B)+P(A\cap B)\] \[P(B)=P(\bar{A}\cap B)\]                       \[[\because P(A\cap B)=0]\] \[=0.3\] \[P(A\cup B)=0.2+0.3=0.5\] \[P(A|A\cup B)=\frac{P(A)}{P(A\cup B)}=\frac{0.2}{0.5}=\frac{2}{5}\] \[P(A|(A\cup B))=\frac{2}{5}\]


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