I'm working on a project for calculating the probability of loot crate drops in a game I play. Here is what I want to calculate:

There is a loot box that has 100 different possible items inside. Each time you open a loot box you can get one of the items, and each item has its own (unknown) probability for dropping out of the loot box. If a large group of people record the number of times they get each item every time they open that crate, eventually we'd get an idea of the probability associated with each item. What is the minimum number of crates we need to open before we can confidently conclude (with alpha=0.05) what the probabilities are?

Thanks!