Suppose we choose three initial centroids x, y, and z, and cluster the points according to which of x, y, or z they are closest. The result will be three apparent clusters, which may or may not coincide with the true clusters A, B, and C. Say that one of the true clusters is correct if there is an apparent cluster that consists of all and only the points in that true cluster. Assuming initial centroids x, y, and z are chosen independently and at random, what is the probability that A is correct