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

  • question_answer
    Let A and B be two events. Then \[1+P(A\cap B)-P(B)-P(A)\] is equal to

    A) \[P(\bar{A}\cup \bar{B})\]

    B) \[P(A\cap \bar{B})\]

    C) \[P(\bar{A}\cap B)\]

    D) \[P(\bar{A}\cap \bar{B})\]

    Correct Answer: D

    Solution :

    [d] we know \[P(A\cup B)=P(A)+P(B)-P(A\cap B)\] Consider; \[1+P(A\cap B)-P(B)-P(A)\] \[=-1-P(B)-P(A)+P(A)+P(B)-P(A\cup B)\] \[=1-P(A\cup B)\]


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