An urn contains N-1 red and 1 green ball. Each ball has an associated weight. If each ball is drawn (without replacement) with a probability proportional to how much its weight contributes to the urn, what is the expected number of attempts required to get the green ball?
Example: 2 red balls of weight 0.3 and 0.4, and green ball of weight 0.3.
In first attempt,
Say, the red ball with weight 0.3 is chosen in the first attempt.
Then, in the next attempt,
Pr(green)=0.3/(0.4+0.3). It becomes relatively difficult to keep track of the probabilities if there are more red balls.