If you have a million coin flips, it’s almost certain that somewhere in those coin flips there will be 20 heads in a row.
My blog post took the Times to task for printing what seemed to be an obviously bogus statement. Since a run of 20 heads is roughly a one-in-a-million occurence, a basic feel for probability should tell you that trying to do this a million times is not going to be a certainty – fairly far from it.
Naturally, I thought to back up my argument with some hard facts, and I came up with a calculation that showed that the chances of this happening were actually around 60%. Unfortunately, I made a pretty basic mistake in calculating the probability, as was demonstrated to me by correspondent Andy Langowitz. My intuition about the likelihood of success was on the money, but my estimate was a bit high.
The story of how I corrected my error in order to get the correct number, around 37.9%, is a good lesson in careful examination of probability rules, with a small detour into the land of the bignum.
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