Coverage when sampling from a non-uniform population

#1
Suppose you have a population of discrete items (e.g. marbles numbered 1 to 100) where the items are each present in different frequencies represented by a Poisson distribution (e.g. at a mean of 50). If randomly sampling from this population (with replacement), how do you calculate how many you need to sample in order to obtain 95% (or some X percentage) of the unique numbers?
 
#3
sounds alot like 'coupon collectors problem'. there was some posts on here a bit ago with problem like this.
Yes I think it's similar, but the population of coupons here is known to be represented at a frequency according to the Poisson distribution. How can the coupon collector solution be modified to account for this distribution?