You have three sets of 100 cards—either all aces, no aces, or exactly one ace; all three are equally likely. You lay the cards out in front of you.
I either (a) ask you whether you’ve got an ace, and you say yes, or (b) turn over one card chosen at random, and find that it’s an ace.
In both cases I now know that you’ve got at least one ace, but the posterior probability that you have all aces is 1⁄2 in case “a” , and (I think) 100⁄101 in case “b”.
You have three sets of 100 cards—either all aces, no aces, or exactly one ace; all three are equally likely. You lay the cards out in front of you.
I either (a) ask you whether you’ve got an ace, and you say yes, or (b) turn over one card chosen at random, and find that it’s an ace.
In both cases I now know that you’ve got at least one ace, but the posterior probability that you have all aces is 1⁄2 in case “a” , and (I think) 100⁄101 in case “b”.