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I feel like I must be missing something, although I suppose all good paradoxes give you that feeling. If it's heads, she's asked once (Monday) what it was, if t
by sysop073 18y ago
I feel like I must be missing something, although I suppose all good paradoxes give you that feeling. If it's heads, she's asked once (Monday) what it was, if tails, she's asked twice (Monday and Tuesday). Therefore, if she has no idea which of the three states she's currently in, there's a 1 in 3 chance it was heads
- psyklic 18y agoThere are three states, but they are not equiprobable. One-half of the time she'll be asked once, and one-half of the time she'll be asked twice. Hence, the one-half argument is because she'll only be in the "once" (Heads) state 1/2 of the time.
- zasz 18y agoThey are equiprobable. When the coin is flipped, it is 50% likely that it will be heads or tails. When it's tails, Beauty must be interviewed again. Therefore, the number of times she's in the state Monday+tails is equal to the number of times she's in the state Tuesday+tails. However, the number of times she's in the state Monday+tails is equal to the number of times she's in the state Monday+heads. No other possible states can occur, so these three states are equiprobable. The answer is that at any point in time, absent other information, the coin is equally likely to be heads or tails, but as soon as Beauty receives the new information that she's being interviewed, it changes the known information, making it 1/3 instead of 1/2.
- psyklic 18y agoThe three states are not equiprobable. Suppose that she must say instead which particular state she is most likely to be in: M+T, T+T, or M+H. Well, we know that Heads is chosen 1/2 of the time, so she should choose M+H! After all, the probability she is in M+T is only 1/4, and the probability she is in T+T is only 1/4. (Since Tails is chosen 1/2 of the time.)