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Manipal Engineering Manipal Engineering Solved Paper-2009

  • question_answer
    If\[A\]and\[B\]are events of a random experiment such that\[P(A\cup B)=\frac{4}{5},\,\,P(\bar{A}\cup \bar{B})=\frac{7}{10}\]and\[P(B)=\frac{2}{5}\], then\[P(A)\]equals

    A) \[\frac{9}{10}\]                                

    B) \[\frac{8}{10}\]

    C) \[\frac{7}{10}\]                

    D)        \[\frac{3}{5}\]

    Correct Answer: C

    Solution :

    Given,\[P(\bar{A}\cup \bar{B})=P(\overline{A\cap B})=\frac{7}{10}\] Since,\[P(A\cap B)+P(\overline{A\cap B})=1\] \[\Rightarrow \]               \[P(A\cap B)=1-\frac{7}{10}=\frac{3}{10}\] Also,      \[P(A\cup B)=P(A)+P(B)-P(A\cap B)\] \[\Rightarrow \]               \[\frac{4}{5}=P(A)+\frac{2}{5}-\frac{3}{10}\] \[\Rightarrow \]               \[P(A)=\frac{4}{5}-\frac{2}{5}+\frac{3}{10}\]                 \[=\frac{2}{5}+\frac{3}{10}=\frac{7}{10}\]


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