Probability of coin flipping streaks.

[Dmobb Jr.]

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"

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.

 

[mathman]

Try google "coin flip streaks". One entry "Introduction to algorithms - page 112" might help.

 

[D H]

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.