What is the Probability of Prisoner A Being Freed in this Situation?

[thamwenyin]

There are three prisoners A,B and C,one of them will be randomly picked by the king to be freed,two others will be executed. The king wants the guard to keep secret on who will be freed. A,who wants to know whether he himself will be freed asks the guard,who,between B and C will be executed. The guard hence told A,"B will be executed",thinking that he gives no useful information to A since at least one of B or C will be executed. From prisoner A point of view,does the probability of him being freed changed before and after the guard tell him the information? Could anyone explain how to do this question? I don't understant the sample answer found from the net.

 

[kmwest]

Here's how I view it. The possibilities are:

1)BC executed, A free
2)AC executed, B free
3)AB executed, C free

Knowing that B will be executed means only scenarios 1 and 3 are possible so P(execution)=P(survival)=1/2.

Note that the Wikipedia rendering of this problem is different than your wording so I don't think your wording is equivalent to the Monty Hall problem.