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Math Help - Dice probability

  1. #1
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    Dice probability

    Three fair six-sided dice are tossed. what is the probability that the sum of the numbers on the two dice equals the number on the third die?


    Can someone help me with this please?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by smoothi963 View Post
    Three fair six-sided dice are tossed. what is the probability that the sum of the numbers on the two dice equals the number on the third die?


    Can someone help me with this please?
    Suppose the dice are distingishable and we start by asking what is the
    probability that die 1 is equal to the sum on die 2 and die 3.

    The table below shows all the ways this can be done.

    Code:
    Die1            Die2           Die3
    2                  1               1
    3                  1               2
    3                  2               1
    4                  1               3
    4                  3               1
    4                  2               2
    5                  1               4
    5                  4               1
    5                  2               3
    5                  3               2
    6                  1               5
    6                  6               1
    6                  2               5
    6                  5               2
    6                  3               3
    There are 15 ways that this can occur. In addition there are 15 ways that
    die2 can be equal to the sum of die1 and die3, and 15 ways that die3 can
    be the sum of die1 and die2. That's a total of 45 ways out of a total of
    6^3 different equaly likley results so the the required probability is:

    p = 45/6^3 = 5/24 ~= 0.208

    RonL
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