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J & K CET Engineering J and K - CET Engineering Solved Paper-2012

  • question_answer
    The probability that atleast one of the events A and B occurs is \[0.5\]. If A and B occur simultaneously with probability \[0.2,\] then \[P({{A}^{c}})+P({{B}^{c}})\]is equal to

    A)  \[1.0\]             

    B)  \[1.1\]

    C)  \[0.7\]             

    D)  \[1.3\]

    Correct Answer: D

    Solution :

    Given, \[P(A\cup B)=0.5\] and \[P(A\cap B)=0.2\] \[\therefore \]    \[P({{A}^{c}})+P({{B}^{c}})=1-P(A)+1-P(B)\] \[=2-\{P\,(A)+P(B)\}\] ?..(i) \[\because \]  \[P(A\cup B)=P(A)+P(B)-P(A\cap B)\] \[\therefore \] \[0.5=P(A)+P(B)-0.2\] \[\Rightarrow \] \[P(A)+P(B)=0.7\] \[\therefore \] From Eq. (i), \[P({{A}^{c}})+P({{B}^{c}})=2-0.7\] \[=1.3\]


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