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

  • question_answer
    If A, B, C are events such that \[P(A)=0.3,P(B)=0.4,P(C)=0.8,P(A\cap B)\]\[=0.08,P(A\cap C)=0.28\] \[P(A\cap B\cap C)=0.09\]. If \[P(A\cup B\cup C)\ge 0.75\] then find the range of \[x=P(B\cap C)\] lies in the interval

    A) \[0.23\le x\le 0.48\]

    B) \[0.23\le x\le 0.47\]

    C) \[0.22\le x\le 0.48\]

    D) None of these

    Correct Answer: A

    Solution :

    [a] Since \[P(A\cup B\cup C)=P(A)+P(B)+P(C)\] \[-P(A\cap B)-P(B\cap C)-P(C\cap A)+P(A\cap B\cap C)\] Or \[P(A\cup B\cup C)=0.3+0.4+0.8-(0.08+0.28)\] \[+P(B\cap C)+0.09\] \[F=1.23-P(B\cap C)\] Or \[P(B\cap C)=1.23-P(A\cup B\cup C)\] But we know that \[0\le P(A\cup B\cup C)\,\,1\] Hence \[0.23\le P(B\cap C)\le 0.48\]


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