Which context is relevant depends on the perspective one is taking - the perspective of the independent observer or the awakened Beauty. — Andrew M
when you get right down to it: it is still just a coin flip. — Jeremiah
And when I see the word "just" used as it is here — Srap Tasmaner
If ever a coin flip wasn't "just" a coin a flip, surely it's Sleeping Beauty. — Srap Tasmaner
I don't think we should assume, for instance, that Beauty is informed by being awakened. — Srap Tasmaner
Can we just get back to SB now? — Srap Tasmaner
Beauty can either consider the probability based on the three possible awakenings that include an interview, or she could consider the coin flip, because regardless of any other considerations, a coin flip is still just a coin flip. Those are the only two relevant sample spaces. — Jeremiah
Mon Tue Heads 1/4 1/4 Tails 1/4 1/4
Mon Tue Heads 1/3 0 Tails 1/3 1/3
There are a couple of curiosities here:
in the first (and perhaps only) interview, heads is twice as likely as tails;
there aren't half as many second interviews as firsts, but one third.
I find these proportions strange. Lewis ends up here and shrugs. I'm not sure what to make of it, but this is a far cry from the way I think halfers want to think of their position, that it's just a coin flip with some meaningless frosting on it. — Srap Tasmaner
Whichever position we take, something about it is counterintuitive. — Srap Tasmaner
When you see Lewis assign 1/4 to T1 and 1/4 to T2 then what are looking at is the frequency in which is he assigning to those two possible outcomes from the 1/2 in the event of tails. He saying that since being awakened on Monday and Tails and Tuesday and Tails is under the same event then you are equally likely to be in either one upon being awakened and interviewed. However, that does not mean they are pulled from a separate sample space. You have to understand that Monday Tails and Tuesday Tails are pulled from the same event of the coin landing on tails, which is 1/2. — Jeremiah
I'm suggesting that we should start with a background sample space that includes all possible combinations of days and coin toss outcomes and then assign probabilities according to a principle of indifference. — Andrew M
You forgot Heads and Wednesday, Heads and Thursday, Heads and Friday. . . . . and on forever.
Then do the same with Tails. — Jeremiah
And in the process don't forget the terms on the days Beauty will be awakened AND interviewed (AKA the sample space), was defined before the experiment started. — Jeremiah
. But since the probabilities are all equal, it doesn't matter how large the background sample space is (at least in a finite universe). — Andrew M
Oh really? So you think they are the same thing. — Jeremiah
Mon Tue Heads 1/3 Tails 1/3 1/3
H has one element and set T has two elements, each with a 50% chance of being selected. — Jeremiah
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