Three Badges and One Guess
Three traders are each given a badge, coloured red or blue by an independent fair coin flip. Each of them can see the other two badges but not their own. At a signal, all three simultaneously either name a colour or say "pass" -- no communication of any kind once the badges are on.
The team wins a shared prize if **at least one person guesses and every guess made is correct**. They may agree on a strategy beforehand. What is the best they can do?
Since any individual guess is a fair coin flip, is the ceiling?
Answer
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