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

  • question_answer
    The probabilities of two events A and B are given as \[P(A)=0.8\] and \[P(B)=0.7.\] What is the minimum value of \[P(A\cap B)?\]

    A) 0

    B) 0.1

    C) 0.5

    D) 1

    Correct Answer: C

    Solution :

    [c] As we know \[P(A\cup B)\le 1\] \[\therefore P(A)+P(B)-P(A\cap B)\le 1\] \[\Rightarrow 0.8+0.7-P(A\cap B)\le 1\] \[\Rightarrow P(A\cap B)\ge 1.5-1\] \[\Rightarrow P(A\cap B)\ge 0.5\] Hence, the minimum value of \[P(A\cap B)\] is 0.5.


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