# Questions tagged [coupon-collector-problem]

In probability, the coupon collector's problem models "collect all the coupons and win" contests. In its simplest form, suppose n distinct types of coupon are equally likely to occur: what is the expected number of coupons we must draw to collect at least one of each type?

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### How often do you have to roll a 6-sided die to obtain every number at least once?

I've just played a game with my kids that basically boils down to: whoever rolls every number at least once on a 6-sided die wins. I won, eventually, and the others finished 1-2 turns later. Now I'm ...
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### How many stickers do I need to complete my FIFA Panini album?

I'm playing the FIFA Panini Online Sticker Album, which is an Internet adaption of the classic Panini albums that are usually published for the soccer world cup, European championship, and possibly ...
581 views

### Mars attack (probability to destroy $n$ spaceships with $k \cdot n$ missiles)

Suppose Earth has been attacked by $n$ Martian spaceships and suppose that we have $m=k \cdot n$ missiles to release against the $n$ spaceships. The probability to hit and destroy each spaceship by ...
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### Probability associated with experiencing all outcomes

Assume last year I commuted to work in a taxi, and suppose if there are $n$ taxis in the fleet I used. If I took one of these taxis every trip at random and with replacement, then what is the number ...
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### Estimating population size from the frequency of sampled duplicates and uniques

There is a web service where I can request information about a random item. For every request each item has an equal chance of being returned. I can keep requesting items and record the number of ...
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### Estimating n in coupon collector's problem

In a variation on the coupon collector's problem, you don't know the number of coupons and must determine this based on data. I will refer to this as the fortune cookie problem: Given an unknown ...
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5k views

### Is there a formula for a general form of the coupon collector problem?

I stumbled across the coupon collectors problem and was trying to work out a formula for a generalization. If there are $N$ distinct objects and you want to collect at least $k$ copies of each of ...
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### Intuition about the coupon collector problem approaching a Gumbel distribution

The coupon collector's problem Let there be $n$ different types of coupons and we try to collect all of the types. We do this by independent random draws of coupons in which each type of coupon has an ...
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### How many times, in expectation, am I fetching a random sample from a predefined discrete probability distribution of elements?

As part of a simulation that I'm working on, I have a probability distribution over $n$ elements, from which I have to sample a set $S$ of size $m$. That is, each element $e \in S$ must be unique [1]...
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### An interesting problem - fishing distribution

I found an interesting problem (not homework) that I can't solve. Lake has 4 types of fishes (A, B, C, D) each with given probability to be caught (0.1, 0.2, 0.3, 0.4). We fish until we catch at least ...
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### Finding a discrete distribution for the minimum number of times needed for all events to occur

Is there a distribution that describes the number of trials before all the events of a random variable with a discrete uniform distribution occurs? Examples: The number of rolls before getting all ...
104 views

### How many samples do I need to take to expect I have seen (x%, say 99%) of the finite population?

Let's say I have balls numbered 1 to 100 in an urn. Every time I pick one at a random, record it as seen and put it back in the urn. How many such picking do I have to perform if I expect to see at ...
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