A Repeated Face
A fair six-sided die is rolled repeatedly until some face appears for the second time (any face that has already appeared). What is the expected number of rolls, including the final one? Give a reduced fraction (a decimal rounded to two or three places is also accepted).
Related problems & prerequisites
Worth solving first
- De Méré's Wager 4.0/10
- The Rendezvous 4.0/10
- Distinct Faces 2.0/10
Source: Birthday-problem variant in wide circulation; no traceable original source. Statement written for AxiomIQ.