The three prisoners and the talkative guard
Three prisoners, A, B and C, are told that exactly one of them, chosen at random, will be pardoned tomorrow. The guard knows who it is.
Prisoner A says to the guard: "At least one of B and C will not be pardoned. Telling me which one is not pardoned gives me no information about my own fate, so please name one." The guard agrees and says, "B will not be pardoned."
A is delighted: "Now it is between me and C, so my chance has risen from one third to one half."
- Is A right? What is A's chance of being pardoned after hearing the guard?
- What is C's chance?
Assume that if A is the one to be pardoned, the guard names B or C with equal probability.
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List the three equally likely worlds (A pardoned, B pardoned, C pardoned) and in each one work out how likely the guard is to say "B".
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