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J & K CET Engineering J and K - CET Engineering Solved Paper-2005

  • question_answer
    The probability that at least one of the event A and B occurs is \[0.6\]. If A and B occur simultaneously with probability \[0.2,\] then \[P(\bar{A})+P(\bar{B})\]is equal to

    A)  \[0.4\]           

    B)  \[0.8\]

    C)  \[1.2\]           

    D)  \[1.4\]

    Correct Answer: C

    Solution :

    Given,  \[P(A\cup B)=0.6\] and \[P(A\cap B)=0.2\] \[\because \] \[P(A\cup B)=P(A)+P(B)-P(A\cap B)\] \[\Rightarrow \] \[P(A)+P(B)=P(A\cup B)+P(A\cap B)\] \[\Rightarrow \] \[1-P(\bar{A})+1-P(\bar{B})=0.6+0.2\] \[\Rightarrow \] \[1-P(\bar{A})+1-P(\bar{B})=0.6+0.2\] \[\Rightarrow \] \[P(\bar{A})+P(\bar{B})=1.2\]


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