I'm trying to solve a probability problem within the context of a Trading Cards game, but I'm not sure if using Hypergeometric Distribution is the right way.
Given the following conditions:
- Given a population size of N=1500 cards: 5 different Team Cards x 10 copies x 30 Teams
- To win the game, a user needs to collect all m=5 Cards of a chosen Team (e.g. Team A)
- User can buy only packs of 5 Cards per time (n=5 permitted draws)
- Packs have no duplicated cards.
- Cards are equally distributed across Packs.
By using the Excel Formula:
=HYPGEOMDIST(k,n,m,N)
the probability to pick 1 Team card by purchasing k=1 Pack should be 14.59%
By making the product of the probabilities, the probability to complete a set of 5 team cards by purchasing 5 Packs should be 14.59%^5 = 0.01%
If all above is correct, I'm still wondering how to find the number of packs I would need to buy, given a certain target p probability to complete the set. E.g. If I wanted a target p = 50% or p = 99% or p = 100% probability of completing the m = 5 Cards Team set, how many packs shall I buy?
I'm adding here the excel with the data, hope it helps! https://docs.google.com/spreadsheets/d/1B-sRhDB_DGmPbGpL-4BD0fzVPJ01dUMlD950seoGMk4/edit?usp=sharing