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Probability Tricks You Every Time
Having the same birthday to have probability less than a half. The easiest way to do the sum is to turn it round and say how many people need to be in a room for none of them having no birthday. When you start doing that sum where the top part of the fraction goes down by one each time, you find that it drops below a half much, much quicker than you expect. And actually at 23, it comes out at slightly less than 50. I think the point about this is it shows how counterintuitive probability can be. Probability tricks you every time.