Linked Questions

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How to calculate the expected value of the coupon collector problem if we are collecting the coupons in groups of k? [duplicate]

The problem: There are n different kinds of coupons, and we need to get every kind of coupon at least once to win. Each time we get new coupons we get them in a batch of k coupons where k ≤ n (the ...
2
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0answers
209 views

Extension to Classical Coupon Collectors Problem [duplicate]

If there's n different coupons. Instead of ordering coupons one-by-one until you collect all n coupons as in the traditional 'Coupon Collector Problem', what if the coupons came in packs of m coupons. ...
1
vote
0answers
21 views

Sample all the elements at least once, with replacement [duplicate]

$s$ balls are sampled and then replaced from/into a box with $N$ balls. On average, how many samplings are to be made until all of the balls have been taken at least once? ps: this is not a homework ...
32
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5answers
596 views

Iteratively replacing $3$ chocolates in a box of $10$

In the fridge there is a box containing 10 expensive high quality Belgian chocolates, which my mum keeps for visitors. Every day, when mum leaves home for work, I secretly pick 3 chocolates at random, ...
22
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1answer
9k views

Probability distribution in the coupon collector's problem

I'm trying to solve the well known Coupon Collector's Problem by explicitly finding the probability distribution (so far all the methods I read involve using some sort of trick). However, I'm not ...
5
votes
3answers
3k views

Probability - Expected number of draws to get all 52 cards at least once drawing in groups of size n [duplicate]

Imagine you have a deck of cards and want to be fairly sure that you draw each card once (with a perfectly fair, complete, and random deck on each draw, of course). You are drawing cards in groups of ...
4
votes
2answers
2k views

Coupon Problem generalized, or Birthday problem backward.

I want to solve a variation on the Coupon Collector Problem, or (alternately) a slight variant on the standard Birthday Problem. I have a slight variant on the standard birthday problem. In the ...
2
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2answers
739 views

coupon collector problem with groups

I was looking at various extensions of the classical Coupon Collector problem, but couldn't find any answers or hints for the following modification: Assume there are $n$ distinct coupons and you get ...
2
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2answers
206 views

Coupon Collecting Problem: $4$ coupons with $p_1 = p_2 = \frac{1}{8}$ and $p_3 = p_4 = \frac{3}{8}$

This is from Ross. I know how to solve everything but (d). The book answer is $\frac{123}{35}$. There are $4$ different types of coupons, the first $2$ of which compose one group and the second $2$...
2
votes
2answers
197 views

Expected number of draws of m objects at a time out of n objects with replacement

The question is as follows: Consider an urn of n distinct objects. At each time, m (m < n) objects are drawn randomly at once. The objects obtained are noted and then placed back in the urn. What ...
1
vote
1answer
234 views

Collecting Stickers! Evaluate occurrence of duplicates?

The Sticker Collector You need to collect $n>1$ different Stickers. Each day you get one pack with $1$ random sticker until you don't collect at least one of each kind. * Each sticker ...
0
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1answer
126 views

How many sticker packets do I need to complete an album?

This question solves the problem of "how many packets do I need to achieve a certain probability of completing the album?", but this made me think of another (quite related) question. Given an album ...
2
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1answer
138 views

YACCP: Coupon collector: Pull 20 coupons per time

Yet-another-coupon-collector's-problem: I know this may be a very similar question to others, but I couldn't crack it and this one has a 'special knack' to it, please bear with me: 260 specific ...
0
votes
1answer
38 views

The probability of getting $y$ new coupons from a batch of $k$

In the coupon collector process, the goal is to assemble a collection of $n$ distinct coupons, while we get a random coupon at each time. I am looking at a generalization of this problem, where at ...