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

  • question_answer
    If A and B be two independent events such that \[P(A)=\frac{2}{3}\]  and \[P(B)=\frac{1}{5},\] the \[P(A\cup B)\]equals to

    A)  \[\frac{1}{15}\]

    B)  \[\frac{11}{15}\]

    C)  \[\frac{2}{15}\]

    D)  \[\frac{13}{15}\]

    Correct Answer: B

    Solution :

    \[\because \]  \[P(A\cup B)=P(A)+P(B)-P(A\cap B)\] \[=P(A)+P(B)-P(A)-P(B)\] (\[\because \] A and B are independent events) \[=\frac{2}{3}+\frac{1}{5}-\frac{2}{3}\times \frac{1}{5}\] \[=\frac{10+3-2}{15}=\frac{11}{15}\]


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