Distinct faces in five rolls

A fair die is rolled 5 times. What is the expected number of distinct faces that appear? Give a decimal to four places.

Show hints (2)+
  1. Indicator that each face shows up at least once.
  2. P(face appears)=1−(5/6)5P(\text{face appears})=1-(5/6)^5.

Answer

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3.5887 (± 0.001)

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