In this paper, we give tight approximation algorithms for the k-center and matroid center problems with outliers. Unfairness arises naturally in this setting: certain clients could always be considered as outliers. To address this issue, we introduce a lottery model in which each client is allowed to submit a parameter indicating the lower-bound on the probability that it should be covered and we look for a random solution that satisfies all the given requests. Out techniques include a randomized rounding procedure to round a point inside a matroid intersection polytope to a basis plus at most one extra item such that all marginal probabilities are preserved and such that a certain linear function of the variables does not decrease in the process with probability one.