Identifying a Truth-Teller With One Question
Two people answer yes/no questions. Person $A$ always tells the truth. Person $B$ answers randomly -- independently saying "yes" or "no" with probability
/2$ each, regardless of the question asked. You do not know which person is $A$ and which is $B$.
You may ask exactly one yes/no question to exactly one person.
1. Construct a question that lets you identify the truthful person with probability strictly greater than
/2$.
2. Compute that probability of correct identification.
3. Prove that your strategy is optimal -- no single yes/no question to one person can do better.
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