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wedrifid comments on Procedural Knowledge Gaps - Less Wrong
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97% seems high. Same sex groups are relatively common. Even if the expected number of women out of the next five people is 2.5 there is probably more than 3% chance of the next five being male.
But then again, more of the people I meet are female than male; I guess those two effects roughly cancel out. Trying to remember when the last few times I met five males in a row were seems to confirm that the number is roughly in the right ballpark. (OTOH, the probability that none of the next five people I met is a man probably is a few times larger than the naive binomial model would predict.)