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Math Help - Dice Probability ?

  1. #1
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    Dice Probability ?

    When rolling 5 dice, what is the probability of rolling at least one 6, one 5, and one 4.
    Is there a Formula Such as P=(1/6)x(1/6)x(1/6)+(1/6)x(1/6). I know the probability
    of rolling one of each with 3 dice is 1/216. I don't know how to compute the
    additional probability of the other two dice. I am looking for the most basic way to do the math.

    Thanks
    Del
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  2. #2
    MHF Contributor undefined's Avatar
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    Quote Originally Posted by Delbert View Post
    When rolling 5 dice, what is the probability of rolling at least one 6, one 5, and one 4.
    Is there a Formula Such as P=(1/6)x(1/6)x(1/6)+(1/6)x(1/6). I know the probability
    of rolling one of each with 3 dice is 1/216. I don't know how to compute the
    additional probability of the other two dice. I am looking for the most basic way to do the math.

    Thanks
    Del
    The simplest thing I can think of is using inclusion-exclusion.

    Let A = event of rolling at least one 6, one 5, and one 4.

    Let C = event that a 6 is not rolled.
    Let D = event that a 5 is not rolled.
    Let E = event that a 4 is not rolled.

    Then by inclusion-exclusion,

    \displaystyle P(\overline{A}) = P(C) + P(D) + P(E) - P(C\cap D) - P(C\cap E) - P(D\cap E) + P(C \cap D \cap E)

    Then you take \displaystyle P(A) = 1 - P(\overline{A})

    P(C) = P(D) = P(E) = ? (think about it)
    P(C ∩ D) = P(C ∩ E) = P(D ∩ E) = ? (think about it)
    P(C ∩ D ∩ E) = ?

    See how far you can get.
    Last edited by undefined; July 19th 2010 at 07:41 PM.
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