I refuse to ignore the labels! :-) Drawing the first math problem tells me a lot, because it’s much more likely in a world with 1 math problem than in a world with 101 math problems. That’s the whole point. It’s not equivalent to drawing a math problem and refusing to look at the label.
Let’s return to the original formulation in your post. I claim that being shown P(1) makes W=0 much more likely than W=1. Do you agree?
If I know that it’s P(1), and I know that it was randomly selected from all the generated problems (rather than being shown to me because it’s the first one), then yes.
If I’m shown a single randomly selected problem from the list of generated problems without being told which problem number it is, it doesn’t make W=0 more likely than W=1 or W=2.
I refuse to ignore the labels! :-) Drawing the first math problem tells me a lot, because it’s much more likely in a world with 1 math problem than in a world with 101 math problems. That’s the whole point. It’s not equivalent to drawing a math problem and refusing to look at the label.
Let’s return to the original formulation in your post. I claim that being shown P(1) makes W=0 much more likely than W=1. Do you agree?
If I know that it’s P(1), and I know that it was randomly selected from all the generated problems (rather than being shown to me because it’s the first one), then yes.
If I’m shown a single randomly selected problem from the list of generated problems without being told which problem number it is, it doesn’t make W=0 more likely than W=1 or W=2.