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- Solution to the sleeping beauty problem: 1/2.
- Why?
- HEADS monday (A)
- /
- coin flip <
- \
- TAILS monday (B) tuesday (C)
- A, B and C are NOT independent cases as it might seem and suggest the 1/3
- answer, because cases B and C aren't independent: if B happens, C happens as
- well and vice versa, if C happens, B happens as well. So B and C are in fact a
- single outcome. Whether we are awoken at B or C is just a subcase of TAILS and
- is irrelevant to reasoning about the coin flip. The credences are therefore:
- A = HEADS = 1/2
- B = C = 1/4 = TALIS / 2
- TAILS = B + C = 1/2
- HEADS + TAILS = 1
- Imagine the modified case in which TAILS awakes the bauty a million times. Would
- this make the probability of coin landing HEADS 1/1000001? Certainly not. There
- will be a million more cases of awakening for TALIS, but we can imagine these
- happening simultaneously, as a single awakening, since all of the 1000000
- awakenings are 100% correlated. The probability of correctly guessing the
- sequence number of awakening in the TAILS case will be 1/1000000 but that's a
- completely different question, the original question asks about the coin flip
- credence, which is 1/2.
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