The Warder’s Coin
brainteaser
Arin, Bela, and Corin are awaiting execution. The governor has secretly selected exactly one of them for a pardon, choosing each prisoner with equal probability.
Arin asks a warder, who knows the decision, to name either Bela or Corin who is certain to be executed. The warder must answer truthfully. If both Bela and Corin are due to be executed, he flips a fair coin to decide which name to give; if only one of them is due to be executed, he names that person.
The warder says, “Bela will be executed.”
Given this information and the warder’s stated procedure, what is the probability that Arin is the prisoner who will be pardoned?
Hints
Hint 1
Hint 2
Hint 3
Solution
Commit an attempt to unseal the proof. Write your answer — right or wrong, thinking it through is the point.
What is Arin’s probability of being pardoned?
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