Two urns, one with a single white marble, one with many black marbles; you flip a coin to decide which urn to draw from; even though there are more black marbles than white, the chances of getting the white marble are equal to the chances of getting one of the many blacks. — Srap Tasmaner
The argument I've been making lately seems to be roughly this: if you close your eyes and someone selects a marble and places it in your hand, and if you know there are more black marbles than white, then you can figure it's more likely to be black. Fair enough. — Srap Tasmaner
But if you know they selected the marble in your hand by flipping a coin to select which urn to draw from, you should figure it's just as likely to be the one white as any of the blacks. — Srap Tasmaner
and missing SB's uncertainty about her own state. — Srap Tasmaner
So what if the coin toss doesn’t happen until after the Monday interview? Does that affect your answer? — Michael
According to this parameterisation, it doesn't make sense to ask SB "what Day is Today?" for "Today" isn't a random variable of the sample-space. (Thirders implicitly ask this question). But all that can be talked about, according to this parameterisation, is the state of the coin and whether SB is awoken on both monday and tuesday, and not "what day is today?". — sime
She is more likely to wake up and see a coin showing tails, as she will wake up more often if the coin lands on tails. — PhilosophyRunner
In that case it is more likely that given an instance I wake up I will see the coin has been flipped heads 100 times in a row. — PhilosophyRunner
I flip a coin and if it lands heads I wake you up tomorrow, if it lands tails you never wake you up. If you wake up and are asked the probability the coin landed heads, what would you say? — PhilosophyRunner
1. — Michael
I think the reasoning that leads you to this conclusion is clearly wrong, given that it’s an absurd conclusion. — Michael
In the SB problem it is 1 for heads and 2 for tails. — PhilosophyRunner
I was talking about frequency not probability. — PhilosophyRunner
the probability of you seeing heads when you wake up is conditional on how often you wake up for heads and how often for tails — PhilosophyRunner
Because SB wakes up more on tails, a given wake up event is more likely to be caused by a tail flip that a head flip. — PhilosophyRunner
Under the assumption of SB undergoing amnesia however, her mental state is uncorrelated with her understanding of B series events, and hence uncorrelated with the state of the coin. — sime
if it’s heads 100 times in a row I wake you up 2^{101} times, otherwise I wake you up once
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