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Math Help - Sample space corresponding to rolling a die

  1. #1
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    Sample space corresponding to rolling a die

    An experiment consists of rolling a die until 3 appears, determine how many elements of the sample space correspond to the event that the 3 appears no later than the k-th roll of the die.

    5^0+5^1+5^2+ ... + 5^{k-1} = (5^k-1)/4

    I'm wondering is there any other ways to do this question? Maybe involve complements somehow?

    thanks
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  2. #2
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    Re: Sample space corresponding to rolling a die

    Quote Originally Posted by usagi_killer View Post
    An experiment consists of rolling a die until 3 appears, determine how many elements of the sample space correspond to the event that the 3 appears no later than the k-th roll of the die.
    5^0+5^1+5^2+ ... + 5^{k-1} = (5^k-1)/4
    I'm wondering is there any other ways to do this question? Maybe involve complements somehow?
    I don't think there is a better way.
    If X denotes roll on which the first three appears then P(X = k) = {\left( {\frac{5}{6}} \right)^{k - 1}}\left( {\frac{1}{6}} \right).
    Thanks from usagi_killer
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