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Three prisoners are informed by their jailer that one of them has been chosen at random to be executed, and the other two are to be freed. Prisoner A asks the jailer to tell him privately which of his fellow prisoners will be set free (with the assumption that the jailer will randomize between B and C if A is the unfortunate soul). A claims that there would be no harm in divulging this information, since he already knows that at least one will go free. The jailer refuses by arguing that if A knew, A’s probability of being executed would rise from 1/3 to 1/2 (i.e., there would only be two prisoners left). Who is correct?

Respuesta :

Cricetus

I think that the jailor's reasoning about the probability is correct. A further explanation is provided below.

  • The above and yet there was a maximum of three captives, most of whom had to somehow be carried out. Thus, a specific prisoner's chance of being executed was 1/3.
  • If and when the jailor notifies him of his release, a minimum of approximately two inmates would be executed, the destiny of which is undetermined, and of those same 2 prisoners. Therefore the likelihood of a certain prisoner being executed is 1/2.

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