There are n stars in the sky that are visible. Jack and Marc each count the stars, independently. Each of them never overcounts a star, but they may miss some of the stars (i.e., each of them either counts it exactly once, or not at all; any single star may be counted by both Jack and Marc). The probability that Jack misses any one star is pJ , and the probability that Marc misses one star is pM. Let X be the number of stars that Jack counts, and let Y be the number of stars that Marc counts. Finally, let W be the number of stars that are counted (by Jack or by Marc). What precisely are the distributions of X, Y and W? (If they are named distributions, give the name and the parameters and some justification.)