# Questions tagged [coupon-collector]

A famous problem of probability, where a person samples a set with replacement until every element of the set (i.e. each coupon) has been obtained at least once. Questions deal with the associated probability distribution, proof techniques, etc.

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### Expected numbers of turns to generate k distinct elements

There is a random number generator. It generates numbers between $1$ and $n$ with equal probability. What is the expected number of turns for it to generate k distinct numbers? EDIT: My approach is to ...
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### Infection in a village

Consider the following problem: Suppose a lonely wanderer infected with a virus came into an isolated village with $M$ villagers and stayed there. Every week each of the infected villagers coughs ...
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### Number of tries to get all characters

If I have the following table 10 Common characters 70% chance 5 Uncommon characters 20% chance 2 Epic characters 10% chance How many tries to get all the characters (I can draw duplicates) How many ...
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### Average time taken to collect at least 1 category of cards from 10 cards with replacement

let say there's 10 card in a box, which categorize to: Spade - A, 2, 3, 4, 5 Heart - A, 2, 3, 4, 5 One card is draw at a time with replacement, What is the average time taken to collect at least one ...
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### Solving Coupon's Collector Problem with Unequal Probabilities in Google Sheets

I am creating a game where I want the player to collect 26 letters (A-Z). Each letter has a different weight/probability. How do I calculate how many draws will a player need to collect all 26 letters,...
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### Expected number of games so that every player has been an Imposter in Among Us

Imagine you have $n$ players. In each game, $k$ $(k\leq n)$ players are chosen randomly to do whatever. By game $G$, what is the probability that every player has been chosen at least once? What is ...
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### Distribution for first time to have drawn all colors

Consider an urn with $n=\sum_{i=1}^rn_i$ balls, where $n_i$ represents the number of balls of color $i$ (out of $r$ possible colors). What’s the distribution describing the first time it takes to have ...
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### Find number of red balls after K turns if you paint Q balls from a bag of N distinct ones

This was a question from Infinix Hiring challenge, which ended few days ago. You have N distinct white balls, and want to paint balls in a red color, instead of ...
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### Use Chebyshev inequality to find a least bound for number of purchases in collector's problem

From the classic version of this problem, we know $T_N$, the number of purchases required to collect N distinct coupons has $E(T_N) \approx NlogN$; $V(T_N) \approx N^2\pi^2 /6$. Here I have got a ...