We show how to distribute data at random (not to be confounded with permutation routing) in a coarse grained parallel environment with $p$ processors. Previously known methods were not able to fulfill the three criteria of uniformity, work-optimality and balance among the processors simultaneously. To guarantee the uniformity we investigate the matrix of communication requests between the processors. We show that its distribution is a generalization of the multivariate hypergeometric distribution and give algorithms to compute it efficiently.