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BCECE Engineering BCECE Engineering Solved Paper-2008

  • question_answer
    If A and B are two independent events such that \[P(B)=\frac{2}{7},P(A\cup {{B}^{c}})=0.8,\]then \[P(A)\] is equal to

    A)  0.1                        

    B)         0.2                        

    C)         0.3                        

    D)         0.4

    Correct Answer: C

    Solution :

    Since, \[P(B)=\frac{2}{7}\]and \[P(A\cap {{B}^{c}})=0.8\] \[P({{B}^{c}})=1-\frac{2}{7}=\frac{5}{7}\] We know that, \[P(A\cup {{B}^{c}})=P(A)+P({{B}^{c}})-P(A).P({{B}^{c}})\] \[\Rightarrow \]\[0.8=P(A)+\frac{5}{7}-\frac{5}{7}p(A)\] \[\Rightarrow \]\[0.8=\frac{5}{7}+\frac{2}{7}p(A)\] \[\Rightarrow \]\[5.6-5=2P(A)\] \[\Rightarrow \]\[p(A)=0.3\]


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