There are 10,000 mutual fund managers. 36 claim that they are the best, since their fund beat the relevant index every year for 8 years.

However, you think that markets are efficient and that the average fund manager is as likely to deliver a better performance than the index as to underperform the index, before fees.

1What is the probability that the average single fund managers beats the index 8 years in a row (before fees)?

2How many fund managers would you expect to beat the index 8 years in a row if only luck and no skill was involved?