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OrphanWilde comments on Monty Hall Sleeping Beauty - Less Wrong
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Comments (17)
Only one of those questions is asked in the problem proper. The other is the product of a poor rephrasing or somebody seeking the question to which their incorrect answer ceases to be incorrect.
I don't know / care to track the problem as it was originally formulated. If it's as you say so, then I wholeheartedly agree that the correct answer is 1/3.
It's just nice to be able to reason correctly about this kind of anthropic questions and to be aware that the answer changes (which is not a given in non Bayesian takes on probability).