Given k equally sized clusters, the probability that a randomly chosen initial centroid will come from any given cluster is 1/k, but the probability that each cluster will have exactly one initial centroid is much lower. (it should be clear that having one initial centroid in each cluster is a good starting situation for k-means.) in general, if there are k clusters and each cluster has n points, then the probability, p, of selecting in a sample of size k one initial centroid from each cluster is given by the equation below. (this assumes sampling with replacement.) from this formula we can calculate, for example, that the chance of having one initial centroid from each of four clusters is 4! /44 = 0.0938.