Given S servers sitting behind a load balancer which spreads request according to a uniform distribution, how many requests R do you need to make to be fairly confident that you've hit each server with a request at least once? ("fairly confident" means the probability of hitting each server at least once is greater than some pre-determined confidence threshhold, e.g. P = 0.95)
More General Question
Given a sample space of size S, let a "trial" consist of randomly (uniform distribution) picking an element from the sample space, observing it, and replacing it. What is the probability that within T trials, you will have observed each element in the sample space at least once?
go run main.go
This will produce (to STDOUT) a comma-separated table of probability estimates, where the columns correspond to sample size and the rows correspond to the number of trials. Sample sizes range from 1 to 20, the number of trials range from 1 to 50. Probability estimates are calculated by repeating the experiment 50,000 times and taking the fraction of successes.