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Math Help - Probability Question

  1. #1
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    Probability Question

    Hi guys, first time poster. I hope this section is the most appropriate for my problem - please feel free to move it if it is too basic

    A fair coin is flipped n times.

    What is the probability that there are at least k consecutive heads in these flips?

    If the k-generalisation is making the working awkward then please just solve it for k = 2 because I think I know how to get from there to the general answer.

    Thanks for any help you can give me!
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  2. #2
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    Quote Originally Posted by Freyalise View Post
    Hi guys, first time poster. I hope this section is the most appropriate for my problem - please feel free to move it if it is too basic

    A fair coin is flipped n times.

    What is the probability that there are at least k consecutive heads in these flips?

    If the k-generalisation is making the working awkward then please just solve it for k = 2 because I think I know how to get from there to the general answer.

    Thanks for any help you can give me!
    It looks to me like you want 1 - P(M_n^{(k)} = 0) from Theorem 1 in this paper.

    This was found by googling Bernoulli trials success runs.
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  3. #3
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    Thank you very much.

    My Maths is not marvellous so that paper will need some study but it looks like exactly what I need. I'm glad the problem was nontrivial after all at least.
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