# Probability of coin flipping streaks.

1. May 14, 2013

### 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?

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. May 14, 2013

### mathman

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

3. May 14, 2013

### D H

Staff Emeritus
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.