Sleeping Beauty volunteers to undergo the following experiment and is told all of the following details: On Sunday she will be put to sleep. Once or twice during the experiment, Beauty will be awakened, interviewed, and put back to sleep with an amnesia-inducing drug that makes her forget that awakening.
A fair coin will be tossed to determine which experimental procedure to undertake: if the coin comes up heads, Beauty will be awakened and interviewed on Monday only. If the coin comes up tails, she will be awakened and interviewed on Monday and Tuesday. In either case, she will be awakened on Wednesday without interview and the experiment ends.
Any time Sleeping Beauty is awakened and interviewed, she is asked, 'What is your belief now for the proposition that the coin landed heads?
Now if the coin is fair then P(Heads and Monday) = P(Tails and Tuesday)
Therefore P(Tails and Tuesday) = P(Tails and Monday) = P(Heads and Monday).
It must add up to one, thus the 1/3. — Jeremiah
P (Tails and Monday) and P (Heads and Monday) are mutually exclusive — T Clark
Also, P (Tails and Monday) and P (Tails and Tuesday) are not independent. — T Clark
Also, you left out P (Heads and Not Tuesday). — T Clark
They are the same flip. It is pointless to argue independence. That is like saying I rolled a die and got 4 and it is not independent because I got 4. If the coin is tails she will be awakened on Monday and awakened on Tuesday, therefore they have the same probability. — Jeremiah
The trouble is that we cannot use conditional probabilities.So we want the conditional P(H|A). — Srap Tasmaner
P (Tails and Monday) and P (Tails and Tuesday) are the same flip, Are you really suggesting they have a different chance of occurring when they both occur on the same chance event? — Jeremiah
The possible outcomes:
- - M T
H: A, S
T: A, A
If she is awakened before Wednesday, there is one awake on heads and two awake on tails. Of the possible awakens there is a 1/3 chance it is Monday and heads. — Jeremiah
But now I don't know if that's misdirection too. — Srap Tasmaner
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