And after updating, as well. The first math problem tells you basically nothing, since it happens regardless of the result of the coin flip/generated random number.
Ignore the labels for a minute. Say I have a box, and I tell you that I flipped a coin earlier and put one rock in the box if it was heads and two rocks in the box if it was tails. I then take a rock out of the box. What’s the chance that the box is now empty? How about if I put three rocks in for tails instead of two?
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.
And after updating, as well. The first math problem tells you basically nothing, since it happens regardless of the result of the coin flip/generated random number.
Ignore the labels for a minute. Say I have a box, and I tell you that I flipped a coin earlier and put one rock in the box if it was heads and two rocks in the box if it was tails. I then take a rock out of the box. What’s the chance that the box is now empty? How about if I put three rocks in for tails instead of two?
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.