
Three prisoners — Aaron, Barney, and Chandler are up for parole. The parole board will release exactly two of them, but the prisoners do not know which two. A friend of Aaron who works as a warden knows which two prisoners will be released. Aaron, understanding that it would be unethical to directly ask the warden if he will be released, but thinks of asking for the name of one prisoner other than himself who is to be released. However, He thinks that before he asks, his chances of release are 2/3. But he thinks that if the warden tells him, "Barney will be released," then his own chances of being released would drop from 2/3 to 1/2, since only two prisoners will be released, and either [Aaron and Barney] or [Barney and Chandler] could be the pair. So Aaron ultimately decides not to reduce his chances by asking.
Is Aaron mistaken in his calculations?