The three prisoners

three prisoners problem

Three prisoners are in separate cells and are all sentenced to death. The governor selected one at random to be pardoned. The guard knows who is going to be pardoned but won’t say.

Being cheeky, Prisoner A asks the guard to let him know which of the others -B and C- is going to be executed. “If B is to be pardoned, tell me C’s name. If C is to be pardoned, tell me B’s name. If I’m to be pardoned, flip a coin to decide which name to say.”

The guard tells A that Prisoner B is going to be executed. Prisoner A is thrilled and thinks that his odds of survival have gone up from 1/3 to 1/2, because it went from being between A, B and C to being between just A and C for the pardon. A tells C about this, who is likewise thrilled because he reasons that while A still has a 1/3 chance of surviving, C has a 2/3 chance of being the pardoned one. Who is wrong?

Share this