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Thu, 20 Jul 2006
Flipping coins, corrected
After a million tosses of a fair coin, you can expect that the numbers of heads and tails will differ by about 1,000.In fact, the expected difference is actually !!\sqrt{2n/\pi}!!. For n=1,000,000, this gives an expected difference of about 798, not 1,000 as I said. I correctly remembered that the expected difference is on the order of √n, but forgot that the proportionality constant was not 1. The main point of my article, however, is still correct. I said that the following assertion is not quite right (although not quite wrong either):
Over a million tosses you'll have almost the same amount of heads as tails I pointed out that although the relative difference tends to get small, the absolute difference tends to infinity. This is still true. Thanks to James Wetterau for pointing out my error.
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