Martina McEnroe has two types of serves: a hard serve (H) and a soft serve (S).† The probability that Martina’s hard serve will land in bounds is pH, and the probability that her soft serve will land in bounds is pS. If Martina’s hard serve lands in bounds, there is a probability wH that Martina will win the point. If Martina’s soft serve lands in bounds, there is a probability wS that Martina will win the point. We assume that pH  wS. Martina’s goal is to maximize the probability of winning a point on which she serves. Use dynamic programming to help Martina select an optimal serving strategy. Remember that if both serves are out of bounds, Martina loses the point.