Each box of a certain breakfast cereal contains one of ten different coupons, each with the same probability. We win a prize if we manage to obtain a complete collection of all the different coupons. How long on average do we have to wait? (For example, suppose we draw the following coupons in order: 5, 2, 3, 7, 5, 1, 1, 4, 8, 4, 1, 9, 10, 2, 3, 3, 6. With the last coupon 6, we have completed our collection, and so we stop after 17 steps.)
2026-02-24 06:46:57.1771915617
The coupon collectors problem
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This is a pretty well known problem. I think I'll just direct you here which has the calculation of the expected waiting time to collect all coupons. Let me know if I can explain any of it to you that is not clear.