Thread: 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)?

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.

Originally Posted by Plato

This is the coupon collection problem.

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.)