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Math Help - Dice Probability

  1. #1
    Member rtblue's Avatar
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    Dice Probability

    Question: A dice is rolled six times. Find the probability that a three is rolled exactly twice.

    My thoughts: I thought i could do (1/6)(1/6)(5/6)(5/6)(5/6)(5/6), because (1/6)(1/6) accounts for the two three's, and the (5/6)(5/6)(5/6)(5/6) accounts for the other four rolls, being anything but a three. Apparently this is wrong, because i get: 625/46656, and the correct answer is: 3125/15552.

    Any suggestions? help is appreciated.
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  2. #2
    MHF Contributor harish21's Avatar
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    Use Binomial Distribution.

    n = 6

    x=2

    p=1/6
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  3. #3
    Member rtblue's Avatar
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    i'm sorry, but your explanation is extremely vague. Can you expand on what you are trying to say?
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  4. #4
    MHF Contributor harish21's Avatar
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    I guess you have very less idea about what BINOMIAL DISTRIBUTION is. Have a look at the link..

    The probability mass function of a Binomial distribution is:

    P(X=x) = \dbinom{n}{x} \; p^x \; (1-p)^{n-x}

    The values of n, p, x are given in Post # 2. Find the required probability.

    Is this clear?
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