Problem 2. A bank makes 10 mortgages. Each of them will either be paid back, with probability %, or go into default, with probability %. Zach is a nancial Wizard, and is interested in the probability that at most 1 mortgage defaults. (a) Suppose that the mortgages are mutually independent. What is the probability that at most 1 mortgage defaults? (b) Suppose that rst, the economy will either do well (with probability %) or badly (with probability i) If the economy does well, each mortgage will (mutually independently) be paid back with probability %; if the economy does badly, each mortgage will (mutually independently) be paid back with probability 19. Under this model of the economy doing well or badly, for what probability p is it the case that each mortgage will be paid back with probability %? (c) In the model of the previous part, what is the probability that at most 1 mortgage defaults? Hint: your answer should be between 49.7% and 49.8%