I meant to refer to "the probability that the current day, as Beauty is currently being interviewed, is Monday".
What you just described is a per-awakening probability. Per-awakening, P(Heads) = 1/3, so the proof that P(Heads | Monday) > 1/2 actually only proves that P(Heads | Monday) > 1/3, which is true since 1/2 > 1/3.
Sorry, you lost me completely. I didn't prove that P(Heads | Monday) > 1/2 at all.
Could you say which step (1-6) is wrong, if I am Beauty, and I wake up, and I reason as follows?
The experiment is unchanged by delaying the coin flip until Monday evening.
If the current day is Monday, then the coin is equally likely to land heads or tails, because it is a fair coin that is about to be flipped. Thus P(Heads | CurrentlyMonday) = 1/2.
By Bayes' theorem, which is applicable because it cannot currently be both Monday and Tuesday:
P(Heads) = P(CurrentlyMond
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