Suppose that the true data consists of three clusters, as suggested by the diagram below: There is a large cluster B centered around the origin (0,0), with 8000 points uniformly distributed in a circle of radius 2. There are two small clusters, A and C, each with 1000 points uniformly distributed in a circle of radius 1. The center of A is at (-10,0) and the center of C is at (100). 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 correctif 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? What is the probability that C is correct? What is the probability that both are correct? After computing these probabilities, identify the true statement from the list below. Note: probabilities are rounded to the nearest percent. O O O O b) d) The probability that C is correct is 19% The probability that C is correct is 24% The probability that A is correct is 19% The probability that both A and C are correct is 12%