Expected minimum of two dice

Two fair dice are rolled. What is the expected value of the smaller of the two? Give a decimal to four places.

Show hints (2)+
  1. E[min⁡]=∑kP(min⁡≥k)E[\min]=\sum_k P(\min\ge k).
  2. P(min⁡≥k)=((7−k)/6)2P(\min\ge k)=((7-k)/6)^2.

Answer

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2.5278 (± 0.001)

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