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    Subject

    Quantitative Aptitude

    Topic

    Probability

    A problem is given to three students whose chances of solving it are 1/2, 1/3 and 1/4 respectively. What is the probability that the problem will be solved?

    ক)
    1/4
    খ)
    1/2
    গ)
    3/4
    ঘ)
    7/12

    Explanation

    Let A, B, C be the respective events of solving the problem and A  ‾,  B‾,  C‾\overline{A\;},\;\overline B,\;\overline C  be the respective events of not solving the problem. Then A, B, C are independent event A  ‾,  B‾,  C‾\overline{A\;},\;\overline B,\;\overline C are independent events Now,  P(A) = 1/2 , P(B) = 1/3 and P(C)=1/4 P(A‾)=12,  P(B‾)=23,  P(C‾)=  34P\left(\overline A\right)=\frac12,\;P\left(\overline B\right)=\frac23,\;P\left(\overline C\right)=\;\frac34 P( none  solves the problem) = P(not A) and (not B) and (not C) = P(A‾∩B‾∩C‾)P\left(\overline A\cap\overline B\cap\overline C\right) = P(A‾)P(B‾)P(C‾)P\left(\overline A\right)P\left(\overline B\right)P\left(\overline C\right) [∵  A‾,  B‾,  C‾  are  Independent]\left[\because\;\overline A,\;\overline B,\;\overline C\;are\;Independent\right] =  12×23×34\frac12\times\frac23\times\frac34 = 14\frac14 Hence, P(the problem will be solved) = 1 - P(none solves the problem) = 1−141-\frac14 = = 3/4

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