I'd like to ask a question about the Sleeping Beauty problem for someone that thinks that 1/2 is an acceptable answer.
Suppose the coin isn't flipped until after the interview on Monday, and Beauty is asked the probability that the coin has or will land heads. Does this change the problem, even though Beauty is woken up on Monday regardless? It seems to me to obviously be equivalent, but perhaps other people disagree?
If you accept that these problems are equivalent, then you know that P(Heads | Monday) = P(Tails | Monday) = 1/2, since if it's Monday then a fair coin is about to be flipped. From this we can learn that P(Monday) = 2 * P(Heads), by the calculation below.
This is inconsistent with the halfer position, because if P(Heads) = 1/2, then P(Monday) = 2 * 1/2 = 1.
EDIT: The calculation is that P(Heads) = P(Monday) P(Heads | Monday) + P(Tuesday) P(Heads | Tuesday) = 1/2 P(Monday) + 0 P(Tuesday), so P(Monday) = 2 * P(Heads).
I think that 1/2 is an acceptable answer, and in fact the only correct answer. Basically 1/2 corresponds to SSA, and 1/3 to SIA; and in my opinion SSA is right, and SIA is wrong.
We can convert the situation to an equivalent Incubator situation to see how SSA applies. We have two cells. We generate a person and put them in the first cell. Then we flip a coin. If the coin lands heads, we generate no one else. If the coin lands tails, we generate a new person and put them in the second cell.
Then we question all of the persons: "Do you think you are in th...
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