2k views

### 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 ...
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. ...
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 ...
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, ...
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 ...
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 ...
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 ...
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 ...
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 $2$...
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 ...
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 ...
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 ...
### 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 ...