Why would you think that?The objective Bayesian will say that an already-flipped coin has a 50% probability of being heads, even if it's actually tails, and that my £10 envelope has a 50% probability of being the smaller amount, even if it's actually the larger amount, whereas the frequentist would deny both of these (as far as I'm aware). — Michael
This is not well-defined. It needs re-stating to make it unambiguous. — andrewk
There's a 50% chance of picking the lower-value envelope, and so after having picked an envelope it's in an "unknown state" that has a 50% chance of being either the lower- or the higher-value envelope? — Michael
"My chance of picking the smaller" is just not the same as "the chance of what I picked being smaller", as I've been saying ineffectually for like 3 weeks. — Srap Tasmaner
That's because I disagree with your interpretation of probability. Your reasoning would seem to suggest that there's a 50% chance of a coin flip landing heads, but that after a flip, but before looking, we can't say that there's a 50% chance that it is heads. I think that we can say that. — Michael
Admittedly, in strident moments I have said things like this.
But look at my last post. It's not about interpretations of probability. It's about how conditional probability works, and it can be a little counter-intuitive. — Srap Tasmaner
Your reasoning would seem to suggest that there's a 50% chance of a coin flip landing heads, but that after a flip, but before looking, we can't say that there's a 50% chance that it is heads. I think that we can say that. — Michael
If I'm told that one envelope contains twice as much as the other, and if I pick one at random, am I right in saying before I open it that there's a 50% chance that my envelope contains the smaller amount?1 If so, I must also be right in saying after I open it and see the amount that there's a 50% chance that my envelope contains the smaller amount (assuming I don't know how the values are selected). — Michael
P(lower) = P(lower|5) + P(lower|10) + P(lower|20) = 4/10 + 1/10 + 0/10 = 1/2. — Andrew M
You just telescoped the step of multiplying by the chance of picking that number.
Could put & where you have |. — Srap Tasmaner
I messed up the math — Andrew M
I have a feeling though that Michael will still think that absent knowledge of the distribution, he can turn back to 50% as an assumption. — Srap Tasmaner
I have a feeling though that Michael will still think that absent knowledge of the distribution, he can turn back to 50% as an assumption. — Srap Tasmaner
In this case, it's the fact that the Hotel has countably infinitely many rooms that enables the assumption of equiprobability to hold. — Pierre-Normand
If a loaded coin flips H 9 out 10 times, without that knowledge, an uninformative of 50/50 prior is completely justified. — Jeremiah
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