An urn contains $N_1$ red balls and $N_2$ green balls. Each ball has an associated weight. Each ball is drawn (without replacement) with a probability proportional to how much its weight contributes to the urn.
What is the probability that when we draw $x$ balls, we get $x$ red balls and $0$ green balls?
Example: 2 red balls of weight 0.3 and 0.4, and 2 green ball of weight 0.2 and 0.1.
In first attempt, the probability to get each ball is the following: Pr(red1)=0.3, Pr(red2)=0.4, Pr(green1)=0.2, Pr(green2)=0.1.
- I think this is the multivariate Wallenius' noncentral hypergeometric distribution.
- This is a follow-up question on Urn with non-uniform probabilities