Please SOLVE ALL PARTS of the questions IN DETAIL with EXPLANATION

Problem 6 The prisoner's dilemma. 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 2/3, but after he knows the answer, the probability of being released will become 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