Let's say that I am gifted several boxes, each containing 1 single material inside of them.
The chance of obtaining all possible Materials (A-E) are as follows:
- Material A 5%
- Material B 30%
- Material C 40%
- Material D 15%
- Material E 10%
I need the following materials to make the blanket:
- Material A x4
- Material B x1
- Material C x1
- Material D x0
- Material E x2
The question to answer is, what is the average number of boxes needing to be opened in order to have enough materials to make the blanket??
If anyone knows how to go about tackling this some help would be excellent! I initially tried tackling this problem by (material type needed/material % drop) then added the sum of all these up, but that was clearly the wrong way to do it.
Often, and it is the case here, there is one material that is the rare one. By the time you get enough of that one, you are (almost) guaranteed to have enough of everything else. Here it is A that is rare. You only get it one time in $20$ and you need $4$, so you should expect to need $80$ boxes. By that time you expect $8$ pieces of E and only need $2$, so the chance you don't have your $2$ is pretty small.