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army1987 comments on Open thread, July 28 - August 3, 2014 - Less Wrong Discussion
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For a quick reminder of the power of many independent trials, estimate and then answer the following question:
I have 2 biased coins in my pocket. The first comes up heads with probability 51%, while the second comes up heads with probability 49%. I take a coin out of my pocket, uniformly at random, and flip it a million times. I observe that it comes up heads 508,634 times. What is the probability that it is the first coin?
Very very close to 1, if the trials are truly independent. But (as Jaynes mentioned in PT:TLoS) there are ways of flipping a coin that systematically favour one side over the other, and you might be unwittingly doing something like that. IOW inside the argument the probability that you took the second coin is negligible, but outside the argument it isn't.
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