While simple urn problems - given $x$ green and $y$ black balls, whats the probability if we take $6$ that $2$ will be black etc. are easily solvable with hypergeometric and binomial distribution. Is there a distribution that solves it a general case for example:
Given $1000$ blue, $1200$ green, $2000$ red balls we draw $20$ balls. If at any point the number of green balls drawn cubed minus the number of red balls squared is greater than the number of blue balls to the power of $2,5$ we add to the urn:
- The number of green balls drawn as green
- Twice the number of red balls as red
- Cubed the numbers of blue balls as blue.
What is the probability that at the end the red balls will be more than the green and the blue combined?
Is this solvable?