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Math Help - Probability

  1. #1
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    Probability

    Can anyone help me with the following probability question please:

    18 fair dice are thrown and the uppermost faces are investigated. What is the probability of each face appearing 3 times?
    (That is the outcome will be {1,1,1,2,2,2,3,3,3,4,4,4,5,5,5,6,6,6}.

    Many thanks to anyone who is able to help

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  2. #2
    Moo
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    Hello,

    The probability of each face appearing once is 3/18 = 1/6 (equiprobability)

    If you want this face appear 3 times, it's P( face \cap face \cap face). Because the throws are independent, this probability equals to P(face)^3, that is to say (1/6)^3
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  3. #3
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    Does this mean then that the probability of each face appearing three times is:

    (1/6)^18? (same as (1/6^3)
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  4. #4
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    Quote Originally Posted by smiler View Post
    18 fair dice are thrown and the uppermost faces are investigated. What is the probability of each face appearing 3 times?
    (That is the outcome will be (1,1,1,2,2,2,3,3,3,4,4,4,5,5,5,6,6,6).
    The event (1,1,1,2,2,2,3,3,3,4,4,4,5,5,5,6,6,6) is one 18-tuple out of 6^{18} possible outcomes.
    But that selection of individual outcomes can occur in \frac {18!}{(3!)^6} ways.
    So the overall probability is \frac {18!}{6^{18}(3!)^6}.
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  5. #5
    Moo
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    Woops, am really sorry, i misunderstood the "18 fair dice", thought it was a 18-faces dice :s
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