The Talkative Warden

Three prisoners, A, B and C, are told that exactly one of them, chosen uniformly at random, has been pardoned and the other two will be executed. A asks the warden to name one of B or C who will be executed. The warden never lies and never names the pardoned prisoner. - If B is pardoned, the warden must say "C". - If C is pardoned, the warden must say "B". - If A is pardoned, both B and C are to be executed, and the warden says "B" with probability 3/4 and "C" with probability 1/4. The warden says "B". What is the probability that A is the one pardoned? Give your answer as a reduced fraction.

• bias
• conditional probability
• distributions
• estimation

Source: Variant of the three prisoners problem, popularised by Martin Gardner in Scientific American (1959). Statement written for AxiomIQ.