# Thread: Computing probability of getting desired items from an infinite pool

1. ## Computing probability of getting desired items from an infinite pool

Hello,

the following real life example of personal significance got me curious about what the answer would look like:

Hasbro is currently selling a series of 24 different "My Little Pony" figurines, all sold separately in non-transparent bags with no clue as to which of the 24 ponies are inside. I only want six specific ponies, and the problem is knowing how many bags I would have to buy in order to get, with probability p, at least one of *each* of the six desirable ponies. Assume that there is an infinite supply of bags, and that the pony inside each bag is random. Assume further that I open all bags at once, not going back to the store for more.

To generalize and put the problem in more familiar terms:
Consider a die with n sides, numbered from 1 to n. How many throws must one make in order to have the chance p of getting all numbers [1..k] (where k <= n)?

2. ## Re: Computing probability of getting desired items from an infinite pool

Originally Posted by blackpaws
Hello,

the following real life example of personal significance got me curious about what the answer would look like:

Hasbro is currently selling a series of 24 different "My Little Pony" figurines, all sold separately in non-transparent bags with no clue as to which of the 24 ponies are inside. I only want six specific ponies, and the problem is knowing how many bags I would have to buy in order to get, with probability p, at least one of *each* of the six desirable ponies. Assume that there is an infinite supply of bags, and that the pony inside each bag is random. Assume further that I open all bags at once, not going back to the store for more.

To generalize and put the problem in more familiar terms:
Consider a die with n sides, numbered from 1 to n. How many throws must one make in order to have the chance p of getting all numbers [1..k] (where k <= n)?
This is the coupon collection problem.

3. ## Re: Computing probability of getting desired items from an infinite pool

Originally Posted by Plato
Thanks for the pointer! But I can't fit that description of the coupon collection problem to my particular version. For one, it only seems to describe cases where you collect *any* set of k coupons, rather than a specific set. (k=6 particular ponies!)

(Collecting any 6 distinct coupons is naturally easier than collecting 6 particular distinct ones.)