I have a bag that contains numbered balls:
- Gray balls numbered 1-13
- Green balls numbered 1-13
- Blue balls numbered 1-12
- Purple balls numbered 1-12
- Yellow balls numbered 1-8
Each color of ball has a certain chance of being pulled, lets say:
- Gray: 16%
- Green: 20%
- Blue: 35%
- Purple: 15%
- Yellow 4%
There are multiple copies of each color-number ball in the bag:
- Gray: 29 copies
- Green: 22 copies
- Blue: 18 copies
- Purple: 12 copies
- Yellow 10 copies
For example, this means there are 29 gray number 1 balls, 29 gray number 2 balls, 22 green number 1 balls, etc.
I am looking to be able to calculate the odds of picking a certain number of specific color-number balls for any number of given picks from the bag where you take 5 out at a time, if you get the color-number ball you are looking for, take it out but then replace all of the wrong balls.
For example, the odds of picking 9 purple number 1 balls in 100 attempts. Or picking 3 purple number 1 balls in 100 attempts if 6 purple number 1 balls are already removed.
This probability problem is for calculating the odds of rolling certain units in Teamfight Tactics if you are familiar with the game. Pretty complicated problem to me but maybe not to some of you.