Three prisoners

Three prisoners A, B, C will have exactly one pardoned, chosen uniformly at random. A asks the guard to name one of B, C who will be executed; the guard truthfully names B (choosing fairly between B and C if both are doomed). Given this, what is the probability that A is pardoned? Give your answer as a decimal (to 2 decimals).

Show hints (2)+
  1. The guard never names A, so his answer says nothing new about A.
  2. Apply Bayes' rule with the guard's tie-breaking probability for B vs C.

Answer

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0.33 (± 0.01)

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Asked at: Jane Street, SIG

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