Three prisoners, A, B and C, have been told by their jailer that one of them, chosen at random, will be executed, and the other two will be freed. Prisoner A says to the jailer,“I know that one of the other prisoners must be freed, so why don’t you tell me which of the two it will be, or tell me one name at random if they are both to be freed? It can’t change my chances of being executed.” The jailer replies, “Once I’ve told you a name, that only leaves two people, so your chances of being executed will have gone up to 1 in 2.” Who is right?
Let A = Event that A is executed. Let B and C = " ".
I am now confused about whether I have to define one single event that A is told, or do I define three separate ones, i.e. A is told it will B, A is told it will be C, A is told it will be A (obviously with probability 0).