2. Suppose there are three prisoners. It is announced that two will be executed tomorrow, and one set free. But the prisoners do not know who will be executed and who will be set free. Prisoner A asks the jailer to tell him the name of one prisoner (B or C) who will be executed, arguing that this will not tell him his own fate. The jailer agrees, and says that prisoner B is to be executed.

Prisoner A reasons that before he had probability 1/3 of being freed, and now he has probability 1/2. The jailer reasons that nothing has changed, and Prisoner A’s probability of surviving is still 1/3.

Who is correct, and why? In what ways is this problem similar to, or different from, the Monty Hall problem?