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

  • question_answer
    Let A and B be two events such that \[P(A\cap B')=0.20,P(A'\cap B)=0.15,\]\[P(A'\cap B')=0.1,\] Then \[P(A/B)\] is equal to

    A) 11/14

    B) 2/11

    C) 2/7

    D) 1/7

    Correct Answer: A

    Solution :

    [a] \[P(A\cap B')=P(A)-P(A\cap B)=0.20\] Also, \[P(A'\cap B)=P(B)-P(A\cap B)=0.15\] \[\Rightarrow P(A)+P(B)-2P(A-B)=0.35\] Now, \[P(A'\cap B')=1-P(A\cup B)\] \[\Rightarrow 0.1=1-P(A)-P(B)+P(A\cap B)\] \[\Rightarrow P(A)+P(B)-P(A\cap B)=0.9\] \[\Rightarrow P(A\cap B)=0.9-0.35=0.55\] and \[P(A)=0.75,P(B)=0.70\] Now, \[P(A/B)=\frac{P(A\cap B)}{P(B)}=\frac{0.55}{0.70}\]


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