Problem 3 in your textbook presents three different sample spaces for a horse race with five horses running. Let the horses be designated by the letters A, B, C, D, and E. A more complete characterization of an outcome of the horse race would be to designate which horse finishes in first through fifth places.Now suppose that each order of finish in the horse race is equally likely. (a) What is the probability that horse A wins and B finishes second? (b) What is the probability that horse C finishes last? (c) What is the probability that horse A wins, B finishes second, and horse C finishes last? (d) Are the events "horse A wins and B finishes second" and "horse C finishes last" inde- pendent? Use your answers from parts (a) through (c) to explain why or why not