JEE Main & Advanced Mathematics Question Bank Critical Thinking

  • question_answer
    The probability of happening an event A is 0.5 and that of B is 0.3. If A and B are mutually exclusive events, then the probability of happening neither A nor B is [IIT 1980; DCE 2000]

    A)                 0.6         

    B)                 0.2

    C)                 0.21       

    D)                 None of these

    Correct Answer: B

    Solution :

               \[P(\overline{A}\cap \overline{B})=P(\overline{A\cup B})=1-P(A\cup B)\]            Since \[A\] and \[B\] are mutually exclusive, so            \[P(A\cup B)=P(A)+P(B)\]                 Hence required probability \[=1-(0.5+0.3)=0.2\].


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