The release of two out of three prisoners has been announced. but their identity is kept secret. One of the prisoners considers asking a friendly guard to tell him who is the prisoner other than himself that will be released, but hesitates based on the following rationale: at the prisoner's present state of knowledge, the probability of being released is $\frac{2}{3}$, but after he knows the answer, the probability of being released will become $\frac{1}{2}$, since there will be two prisoners (including himself) whose fate is unknown and exactly one of the two will be released. What is wrong with this line of reasoning?
2026-04-03 11:04:26.1775214266
The Prisoner's Release Probability Problem
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The probability of this prisoner being released is already $0$ or $1$. The prisoner has no agency in determining who is or is not released.