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

  • question_answer
    Let A and B be two events such that \[P(A)=0.3,\]\[P(A\cup B)=0.8,\]if A and B are independent events, then \[P(B)\] is equal to

    A)  \[5/7\]          

    B)  \[5/13\]

    C)  \[1/3\]          

    D)  \[1/2\]

    Correct Answer: A

    Solution :

    Given that, \[P(A)=0.3\] and \[P(A\cup B)=0.8\] We know \[P(A\cup B)=P(A)+P(B)-P(A\cap B)\] \[\Rightarrow \] \[0.8=0.3+P(B)-0.3P\,(B)\] \[[\because \,\,P(A\cap B)=P(A)\,\,P(B)\,\,given]\] \[\Rightarrow \] \[0.5=0.7\,\,P\,(B)\] \[\Rightarrow \] \[P\,(B)=\frac{5}{7}\]


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