Rolls until a face repeats

You roll a fair die repeatedly. What is the expected number of rolls until some face appears for the second time? Give a decimal to four places.

Show hints (2)+
  1. A 'birthday problem' on six faces.
  2. E=∑kP(no repeat in first k)E=\sum_k P(\text{no repeat in first }k).

Answer

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3.7747 (± 0.001)

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