There is a group of portfolio managers who each have a50% chance of beating the market by10% in a given year and a50 % chance of underperforming by 10%. Performance from one year to the next is independent and uncorrelated. Returns are simple returns, and compounding is ignored.

Suppose that unsuccessful managers get forced out of the business as soon as they are down overall 30%- that is, as soon as their record contains 3 more losing years than winning years. What is the probability of failure over a period of 5 years? Express your answer as an exact fraction (i.e. do not enter a real number).

Probability of