With the same assumptions as in Exercise 2, three classes are independently selected at random.
a. Let A denote the event that all three of the classes have 40 or more students (i.e., 40 or more in each class). Find a bound on the probability of A. Hint: Separate A into three independent events, find a bound on the probability of each, and then think about how to appropriately combine your bounds.
b. In the scenario above, let B denote the event that all three classes selected at random will have between 20 and 42 people (i.e., 20 to 42 people in each class). Find a bound on the probability of B. Hint: Again, separate B into three independent events, find a bound on each, and then recombine appropriately.