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J & K CET Engineering J and K - CET Engineering Solved Paper-2003

  • question_answer
    If A and B are two mutually exclusive events then

    A)  \[P(A)<P(\bar{B})\]   

    B)  \[P(A)>P(\bar{B})\]

    C)  \[P(A)<P(B)\]   

    D)  None of these

    Correct Answer: A

    Solution :

    Since, A and B are mutually exclusive events. Then, \[P(A\cup B)=P(A)+P(B)\] \[\Rightarrow \] \[P(A)+P(B)\le 1\] \[\Rightarrow \] \[P(A)\le 1-P(B)\] or \[P(B)\le 1-P(A)\] \[\Rightarrow \] \[P(A)\le P(\overline{B})\] or \[P(B)\le P(\overline{A})\] Hence, option [a] is correct.


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