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What is the probability that rolling four fair, six-sided dice produces an even sum?

  • Math -

    even sum 2, 4, 6, 8 , 10, 12

    ways 1,1 one way
    3,1;2,2; 1,3 three ways
    5,1;4,2;3,3;3,3;1,5;2;4 six ways
    and continue...

    So for the pr (2)=1/6*1/6
    pr(4)=1/6*1/6*3
    pr(6)=1/6*1/6*6
    and continue

  • Math -

    To have an even sum
    1. all four must be even (E)
    2. all four must be odd (O)
    3 two must be even, two must be odd.

    prob that one die lands even = 3/6 = 1/2
    the same as for odd.

    prob of EEEE = (1/2)^4
    prob of OOOO = (1/2)^4
    prob of EEOO = 4!/(2!2!) (1/2)^4

    sum = 1/16 + 6(1/16) + 1/16 = 8/16 = 1/2

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