Subject

    Quantitative Aptitude

    Topic

    Probability

    Four dice are thrown simultaneously. Find the probability that all of them show the same face.

    ক)
    1/216
    খ)
    1/36
    গ)
    2/216
    ঘ)
    4/216

    Explanation

    The total number of elementary events associated to the random experiments of throwing four dice simultaneously is: = 6×6×6×6=646\times6\times6\times6=6^4 n(S) = 646^4 Let X be the event that all dice show the same face. X = { (1,1,1,1,), (2,2,2,2), (3,3,3,3), (4,4,4,4), (5,5,5,5), (6,6,6,6)} n(X) = 6 Hence required probability = n(X)n(S)=664\frac{n(X)}{n(S)}=\frac6{6^4} = 1216\frac1{216}

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