One blue die matches the red

Three fair 66-sided dice are rolled: two are blue and one is red. What is the probability that exactly one of the two blue dice matches the red die's value?

Show hints (2)+
  1. Given the red value, each blue die matches it with probability 1/61/6, independently.
  2. Number of matches is Binomial(2,1/6)(2,1/6); take the "exactly one" term.

Answer

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0.2778 (± 0.001)

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Asked at: Optiver, Akuna Capital

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