(The prisoner’s dilemma) Three prisoners, A, B, and C, are sentenced to death and they have been put in separate cells. All three have equally good grounds to apply for parole and the parole board has selected one of them at random to be pardoned.

The warden knows which one is pardoned, but is not allowed to tell. Knowing this, Prisoner A asks the warden to let him know the identity of one of the others who is going to be executed. “If B is to be pardoned, give me C’s name. If C is to be pardoned, give me B’s name. And if I’m to be pardoned, toss a coin to decide whether to name B or C.”

The warden tells A that B is to be executed. Prisoner A is pleased because he believes that his probability of surviving has gone up from 1/3 to 1/2, as it is now between him and C. Prisoner A secretly tells C the news, who when hearing the news believes that A still has a chance of 1/3 to be the pardoned one, but his chance has gone up to 2/3.

What is the correct answer? Prisoner C is right, A’s probability of surviving is still 1/3, but prisoner C’s probability of receiving the pardon is 2/3. Explain why.