The coupon collector's problem is a classic question in probability theory about how long it takes to collect a complete set of items chosen at random with replacement. It asks, if there are n different types of coupons and one coupon is drawn at random each time, how many draws are expected before every one of the n types has been drawn at least once. Mathematical analysis shows that the expected number of draws needed grows in proportion to n multiplied by the logarithm of n. For example, when there are 50 different coupons, it takes about 225 draws on average to collect all of them. The same problem is often restated in terms of rolling a die with n sides until every face has come up at least once.
Facts
StatementGiven n coupons, how many draws with replacement are expected before each coupon has been drawn at least once. 1 Classification
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Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
In Branch
Source Coupon collector's problem (Wikipedia)
Sources
1. Coupon collector's problem (Wikipedia)
Lead paragraph, equivalent formulation
given n coupons, how many coupons do you expect you need to draw with replacement before having drawn each coupon at least once?
In Branch: Probability and Statistics, Lead sentence
In probability theory, the coupon collector's problem refers to mathematical analysis of "collect all coupons and win" contests.
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