In probability theory, the coupon collector's problem describes the "collect all coupons and win" contests. It asks the following question: Suppose that there are n different coupons, equally likely, from which coupons are being collected with replacement. What is the probability that more than t sample trials are needed to collect all n coupons? An alternative statement is: Given n coupons, how many coupons do you expect you need to draw with replacement before having drawn each coupon at least once? The mathematical analysis of the problem reveals that the expected number of trials needed grows as . For example, when n = 50 it takes about 225 trials to collect all 50 coupons.
Read more about Coupon Collector's Problem: Understanding The Problem, Extensions and Generalizations
Famous quotes containing the words collector and/or problem:
“Though collecting quotations could be considered as merely an ironic mimetism—victimless collecting, as it were ... in a world that is well on its way to becoming one vast quarry, the collector becomes someone engaged in a pious work of salvage. The course of modern history having already sapped the traditions and shattered the living wholes in which precious objects once found their place, the collector may now in good conscience go about excavating the choicer, more emblematic fragments.”
—Susan Sontag (b. 1933)
“I tell you, sir, the only safeguard of order and discipline in the modern world is a standardized worker with interchangeable parts. That would solve the entire problem of management.”
—Jean Giraudoux (1882–1944)