4. Suppose that a set of portfolio managers has a chance p = 50% of beating the market by 10% in a given year and chance 1 - p of underperforming by 10%. Performance from one year to the next is independent and uncorrelated. Returns are simple returns and compounding is ignored. (a) What is the probability that a manager will achieve a five-year track record which beats the market for at least 4 out of 5 years? (b) Suppose that unsuccessful managers get forced out of business as soon they are down overall -30%; that is, as soon as as their record contains 3 more losing years than winning years. What is the probability of failure over a five-year horizon? (c) Among those who survive, what is the expected total return?