That’s a good example. There is a big difference though (it’s subtle). With sleeping beauty, the question is about her probability at a waking. At a waking, there are no duplicate surveys. The duplicates occur at the end.
That is a difference, but it seems independent from the point I intended the example to make. Namely, that a relative frequency can still represent a probability even if its denominator includes duplicates—it will just be a different probability (hence why one can get 1⁄3 instead of 1⁄2 for SB).
That’s a good example. There is a big difference though (it’s subtle). With sleeping beauty, the question is about her probability at a waking. At a waking, there are no duplicate surveys. The duplicates occur at the end.
That is a difference, but it seems independent from the point I intended the example to make. Namely, that a relative frequency can still represent a probability even if its denominator includes duplicates—it will just be a different probability (hence why one can get 1⁄3 instead of 1⁄2 for SB).
Ok, yes, sometimes relative frequencies with duplicates can be probabilities, I agree.