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

  • Thread starter thamwenyin
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In summary, the conversation discusses three prisoners who are awaiting their fate: one will be randomly chosen to be freed by the king, while the other two will be executed. Prisoner A asks the guard who will be executed between prisoners B and C, to which the guard responds that B will be executed. This information does not change the probability of A being freed, as it is still 1/2. The conversation also touches on the Monty Hall problem, but the wording differs from the traditional version.
  • #1
thamwenyin
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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.
 
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  • #2
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.
 

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

1. What is the Three Prisoners Problem?

The Three Prisoners Problem is a mathematical brain teaser that involves three prisoners, A, B, and C, who are sentenced to death. The warden gives them a chance to escape by playing a game. If at least one of them can correctly guess the color of their own hat, they will all be set free. However, if anyone guesses incorrectly, they will all be executed.

2. How does the Three Prisoners Problem work?

The three prisoners are blindfolded and lined up so that each prisoner can only see the hats of the prisoners in front of them. The warden then places either a white or black hat on each prisoner's head. The prisoners cannot see their own hat, but can see the hats of the prisoners in front of them. They must then try to guess the color of their own hat without communicating with each other.

3. What is the optimal strategy for the prisoners?

The optimal strategy for the prisoners is for the first prisoner to guess the color of their own hat based on the number of black hats they can see in front of them. If they see an even number of black hats, they will guess white. If they see an odd number of black hats, they will guess black. The other prisoners will then base their guesses on the previous prisoner's guess and the number of black hats they can see in front of them.

4. Is there a guaranteed solution to the Three Prisoners Problem?

No, there is no guaranteed solution to the Three Prisoners Problem. The optimal strategy gives the prisoners a 50% chance of survival, but it is not a guaranteed solution. It is possible for all three prisoners to guess incorrectly and be executed.

5. What is the significance of the Three Prisoners Problem?

The Three Prisoners Problem is a popular puzzle in mathematics and logic. It demonstrates the importance of strategic thinking and game theory. It also has real-life applications in decision making and problem solving. Many variations of the problem have been proposed and studied, making it a fascinating topic for research and discussion.

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