As I’m a glutton for punishment, here’s another classic.
Out of three prisoners (whose names are Alan, Bill and Charles) scheduled to be put to death, it has been decided that one of them will be pardoned. The pardoned prisoner is chosen randomly.
Alan asks the warden to tell him the name of one of the others who will be executed. The warden is under strict instructions to not reveal the fate of a prisoner to that prisoner. The warden (who knows who is going to be pardoned and speaks truthfully) reveals to Alan that Bill is going to be executed.
What is the probability that Charles is going to be executed?
What is the probabilty that Alan is going to be executed?
Hint: neither probability is 1/2.
Much later (July 2011): The question can only sensibly be answered if you assume that the warden is unbiased. i.e. If Alan is going to be pardoned, it is equally likely that the warden will name Bill or Charles.