4.37 Independence of complements. Show that if events A and B obey the multiplication rule, P(A and B) = P(A)P(B), then A and the complement B^c of B also obey the multiplication rule, P(A and B^c) = P(A)P(B^c). That is, if events A and B are independent, then A and B^c are also independent. (Hint: Start by drawing a Venn diagram and noticing that the events “A and B” and “A and B^c” are disjoint.)