19. Assume the probability of being ranked in the top half of all fund managers when ranked by performance is 50% and is independent of past performance or anything else. That is, assume it is similar to the outcome of a coin flip. (A) What is the probability that a fund manager will be ranked in the top half two years in a row? (B) What is the probability that a fund manager will be ranked in the top half five years in a row? (C) You observe the performance of 100 portfolio managers for 5 years and rank them by investment performance each year. You find that 3 of the funds have investment returns in the top half of the sample each and every year, and conclude that this is evidence that these managers have skill to outperform others. Is your conclusion justified? 19. Assume the probability of being ranked in the top half of all fund managers when ranked by performance is 50% and is independent of past performance or anything else. That is, assume it is similar to the outcome of a coin flip. (A) What is the probability that a fund manager will be ranked in the top half two years in a row? (B) What is the probability that a fund manager will be ranked in the top half five years in a row? (C) You observe the performance of 100 portfolio managers for 5 years and rank them by investment performance each year. You find that 3 of the funds have investment returns in the top half of the sample each and every year, and conclude that this is evidence that these managers have skill to outperform others. Is your conclusion justified