Expected maximum of three dice

Three fair dice are rolled. What is the expected value of the largest? Give a decimal to four places.

Show hints (2)+
  1. Use E[max⁡]=∑kP(max⁡≥k)E[\max]=\sum_k P(\max\ge k).
  2. P(max⁡≥k)=1−((k−1)/6)3P(\max\ge k)=1-((k-1)/6)^3.

Answer

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4.9583 (± 0.001)

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