I think it’s fairly simple, as I’ve encountered this problem before. The odds would be .5 in the terms that “either the coin landed heads or it didn’t”, with (assuming non-partial others) a 1% chance that you’re in the odd room. To you it might seem that it’s .5 because you’re either in a blue room, or you’re not. However, it’s also that you’re either in the odd room, or one of the 99 of the differently coloured ones.
One variant would be that there would be two seemingly identical buildings, one with 99 red rooms and one blue, one with 99 blue rooms and one red. You go into one of the buildings, and fall down a trapdoor into a blue room. The odds that you walked into the building with 99 blue rooms should be 99 %.
With a 99 percent certainty, you can guess what the result of the coinflip was.
I think it’s fairly simple, as I’ve encountered this problem before. The odds would be .5 in the terms that “either the coin landed heads or it didn’t”, with (assuming non-partial others) a 1% chance that you’re in the odd room. To you it might seem that it’s .5 because you’re either in a blue room, or you’re not. However, it’s also that you’re either in the odd room, or one of the 99 of the differently coloured ones.
One variant would be that there would be two seemingly identical buildings, one with 99 red rooms and one blue, one with 99 blue rooms and one red. You go into one of the buildings, and fall down a trapdoor into a blue room. The odds that you walked into the building with 99 blue rooms should be 99 %.
With a 99 percent certainty, you can guess what the result of the coinflip was.