Show that the probability that a will be executed

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Three prisoners, whom we may call A, B, and C, are informed by their jailer that one of them has been chosen at random to be executed, and the other 2 are to be freed. Prisoner A, who has studied probability theory, then reasons to himself that he has probability 1/3 of being executed. He then asks the jailer to tell him privately which of his fellow prisoners will be set free, claiming that there would be no harm in divulging this information, since he already knows that at least 1 will go. The jailer (being an ethical fellow) refuses to reply to this question, pointing out that if A knew which of his fellows were to be set free then his probability of being executed would increase to ½, since he would then be 1 of 2 prisoners, I of whom is to be executed. Show that the probability that A will be executed is still·!, even if the jailer were to answer his question, assuming that, in the event that A is to be executed, the jailer is as likely to say that B is to be set free as he is to say that C is to be set free.

Reference no: EM131832952

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