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Math Help - The chance of doing something given multiple tries

  1. #1
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    The chance of doing something given multiple tries

    I have looked through this topic for almost an hour trying to find this question already answered, forgive me if it has been.

    If I have a fair six sided die and I roll it 20 times
    what is the chance i will roll a 6 at least once?
    What is the chance I will roll a 6 only once?

    I dont need the answer just the formula for the answer.
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  2. #2
    MHF Contributor undefined's Avatar
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    Quote Originally Posted by LordSoth View Post
    I have looked through this topic for almost an hour trying to find this question already answered, forgive me if it has been.

    If I have a fair six sided die and I roll it 20 times
    what is the chance i will roll a 6 at least once?
    What is the chance I will roll a 6 only once?

    I dont need the answer just the formula for the answer.
    Binomial probability - Wikipedia, the free encyclopedia

    For the first, I would take the probability of rolling no 6's and subtract that from 1.
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  3. #3
    MHF Contributor ebaines's Avatar
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    The probability of rolling a 6 at least once = probability of rolling a 6 followed by a non-6, plus probability of rolling a non-6 followed by a 6, plus probability of rolling a 6 followed by a 6:

    1/6 x 5/6 + 5/6 x 1/6 + 1/6 x 1/6.

    Which as Undefined points out is the same as 1 minus the probability of a non-6 followed by a non-6.

    Probability fo rolling a 6 just once can be calculated from the first two terms of the above.
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