The larger die shows a 4 - what about the smaller?

Two fair dice are rolled and you're told that the larger of the two values is exactly 4. What is the expected value of the smaller one? (to 3 decimals)

Show hints (2)+
  1. List the ordered outcomes whose maximum is exactly 4 - they're equally likely.
  2. There are 7: the double (4,4)(4,4) once, and each of 1, 2, 3 paired with a 4 in two orders.

Answer

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2.286 (± 0.005)

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