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Probability of coin flipping streaks.

  1. May 14, 2013 #1
    Recently I was discussing hitting streaks with my dad and I said "If you flip a coin a million time you're bound to get a streak of a hundred."

    I am not sure if this is actually true and I am having some trouble figuring it out.

    The more general question that I would like to be able to answer is what is the probability that you will get a streak of k heads when you flip a coin n times?

    I found this article "http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-042j-mathematics-for-computer-science-spring-2005/lecture-notes/l24_spcl_topics.pdf" [Broken]

    It explaines how to solve this however it requires k base cases. For k=100, this method is kind of useless. Can anyone think of a good way to solve this for large k and n?

    PS. Using a computer is certainly okay.
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. May 14, 2013 #2


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    Try google "coin flip streaks". One entry "Introduction to algorithms - page 112" might help.
  4. May 14, 2013 #3

    D H

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    The probability of rolling 100 heads in a row is 1/2100, or less than 10-30. Multiply this by a million and you still get a ridiculously small number. Note well: This is an upper bound. This simple calculation ignores the fact that there is a chance of getting 101 heads (or more) in a row somewhere along the line.
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