Rolls to a six before a five

You roll a fair die repeatedly until a 66 appears. Given that the first 66 occurs before the first 55, what is the expected number of rolls?

Show hints (2)+
  1. Track the wait until the first 55-or-66: it's Geometric(1/3)(1/3), mean 33.
  2. Which face (5 or 6) comes first is independent of when - so conditioning doesn't change the expected count.

Answer

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Asked at: Jane Street, Akuna Capital

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