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    Subject

    Quantitative Aptitude

    Topic

    Probability

    The probability of success of three students X, Y and Z in the one examination are 1/5, 1/4 and 1/3 respectively. Find the probability of success of at least two.

    ক)
    1/4
    খ)
    1/2
    গ)
    1/6
    ঘ)
    1/3

    Explanation

    P(X) = 15\frac15 ,  P(Y) = 14\frac14 , P(Z) = 13\frac13 Required probability: = [ P(A)P(B){1−P(C)} ] + [ {1−P(A)}P(B)P(C) ] + [ P(A)P(C){1−P(B)} ] + P(A)P(B)P(C) = (14×13×45)+(34×13×15)+(23×14×15)+(14×13×15)\left(\frac14\times\frac13\times\frac45\right)+\left(\frac34\times\frac13\times\frac15\right)+\left(\frac23\times\frac14\times\frac15\right)+\left(\frac14\times\frac13\times\frac15\right) = 460+360+260+160\frac4{60}+\frac{\displaystyle3}{\displaystyle60}+\frac{\displaystyle2}{\displaystyle60}+\frac{\displaystyle1}{\displaystyle60} = 1060\frac{10}{60} = 16\frac16

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