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Coupon collector's problem. In probability theory, the coupon collector's problem refers to mathematical analysis of "collect all coupons and win" contests. It asks the following question: if each box of a given product (e.g., breakfast cereals) contains a coupon, and there are n different types of coupons, what is the probability that more ...
Pages in category "Probability problems" The following 31 pages are in this category, out of 31 total. ... C. Coupon collector's problem; G. Gambler's ruin;
In combinatorics, the twelvefold way is a systematic classification of 12 related enumerative problems concerning two finite sets, which include the classical problems of counting permutations, combinations, multisets, and partitions either of a set or of a number. The idea of the classification is credited to Gian-Carlo Rota, and the name was ...
It is stated that "[The coupon collector's problem] asks the following question: If each box of a brand of cereals contains a coupon, and there are n different types of coupons, what is the probability that more than t boxes need to be bought to collect all n coupons?" However, this question is not answered in the solution section.
Envy-free item allocation. Envy-free (EF) item allocation is a fair item allocation problem, in which the fairness criterion is envy-freeness - each agent should receive a bundle that they believe to be at least as good as the bundle of any other agent. [1] : 296–297.
This phenomenon is closely related to the coupon collector's problem: in order to be connected, a random graph needs enough edges for each vertex to be incident to at least one edge. More precisely, if random edges are added one by one to a graph, then with high probability the first edge whose addition connects the whole graph touches the last ...
Mannequins display the store's new spring fashions at a J.C. Penney store in Queens, New York. (Victor J. Blue/Bloomberg via Getty Images)J.C. Penney's disastrous sales plunge under CEO Ron ...
In network theory, a giant component is a connected component of a given random graph that contains a significant fraction of the entire graph's vertices . More precisely, in graphs drawn randomly from a probability distribution over arbitrarily large graphs, a giant component is a connected component whose fraction of the overall number of ...