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Math Help - Probability of dice landing on '6' for 3rd time on the 20th roll

  1. #1
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    Probability of dice landing on '6' for 3rd time on the 20th roll

    A die is rolled repeatedly:

    1) Find the probability that the 3rd time a '6' shows is on the 20th role.

    2) Generalise to the kth time on the nth roll.
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  2. #2
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    you are bing asked to derive a standard distribution, but i cant remember the name of the thing.

    anyway, Here is a hint to get you started

    part (a)
    Find the chance that there are 2 sixes on the first 19 rolls, and multiply by the chance of getting a 6 on the 20'th roll.

    You can get the probability of 2 6's in 19 rolls by using the bonomial distribution.


    part (b)
    The above argument generalises.



    Can you finish from there?
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  3. #3
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    Quote Originally Posted by SpringFan25 View Post
    you are bing asked to derive a standard distribution, but i cant remember the name of the thing.

    anyway, Here is a hint to get you started

    part (a)
    Find the chance that there are 2 sixes on the first 19 rolls, and multiply by the chance of getting a 6 on the 20'th roll.

    You can get the probability of 2 6's in 19 rolls by using the bonomial distribution.


    part (b)
    The above argument generalises.



    Can you finish from there?
    Yeah thanks. I managed to get the answer with your help.
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