Suppose that there exist two kinds of stars (or raisins in a cake, or flaws in a material). The probability that a given volume contains j stars of the first kind is pj; a), and the probability that it contains k stars of the second kind is p(k; b); the two events are assumed to be independent. Prove that the probability that the volume contains a total of n stars is p(n; a+b). (Interpret the assertion and the assumptions abstractly.)