(e) Suppose that in any given year, there is a 50% chance that a mutual fund will outperform the market simply by chance. If there are N mutual funds, what is the smallest number N such that the probability of observing at least one out of these N funds outperform the market for 10 consecutive years by chance exceeds 99%? Noting that there are around 8,000 mutual funds in the US, comment on the implication(s) of your answer for empirical tests of efficient markets. (5 marks) (e) Suppose that in any given year, there is a 50% chance that a mutual fund will outperform the market simply by chance. If there are N mutual funds, what is the smallest number N such that the probability of observing at least one out of these N funds outperform the market for 10 consecutive years by chance exceeds 99%? Noting that there are around 8,000 mutual funds in the US, comment on the implication(s) of your answer for empirical tests of efficient markets