I play a game where there are loot boxes that follow a probability distribution. In a loot box, you always have 3 loot pieces.
The following information is given:
Chance of ATLEAST 1:
100% - Rare Item or Better
24.8% - Epic or Better
7.4% - Legendary
Every loot box contains at least one "Rare" item or better. The other two items can also be rare, epic, or legendary. But can also be common.
I would like to know the probabilities of each without the "or better" part. As Epic or better means legendary. So for Epic or Legendary, you have a 24.8% chance. Which (If I'm right) gives Epic a chance of 24.8-7.4 = 17.4%
The tricky part is in the common items, which is not given. I thought of calculating it as follows: Common item chance = 1-rare-epic-legendary
In the end, I would like to calculate the expected value of one pack. Can that be done with the given information?
No it cannot be done. For ease of presentation I'll change the probabilities to rounder numbers, but the point remains regardless of actual values of the numbers.
Consider the following 4 boxes:
(R,R,R) (R,R,E) (R,R,E) (R,R,L)
compared to the other 4 boxes
(R,R,R) (R,E,E) (R,E,E) (R,E,L)
in both cases, the probability of getting at least 1 E or better is 75%, and the probability of getting at least 1 L is 25%. But in the first, the probability getting at least 1 E is 50%, while in the second it is 75%.