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timtyler comments on Beauty quips, "I'd shut up and multiply!" - Less Wrong
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She knows in advance how many times she will be woken up (on each coin result). It says so in the problem description. So, she never answers 1/2 in the first place. She doesn't update on awakening. She updates when she is told the experimental procedure in the first place.
So, in the extreme sleeping beauty problem, when she is told the experimental procedure, she decides that it will be tails with near certainty?