Q. Much is made over the fact which some mutual funds outperform the market year after year. Which is, the return from holding shares in the mutual fund is higher than the return from holding a portfolio such as the S&P 500? Suppose there are 5000 mutual funds in which you can invest. Suppose each has a probability of 0.5 of outperforming the market in any given year also which performance in each year is independent of performance in any other year?

a. Illustrate what is the probability which any particular fund outperforms the market in 5 consecutive years, 10 consecutive years and 20 consecutive years?

b. Illustrate what is the probability which at least one of the 5000 funds outperforms the market in 5 consecutive years, 10 consecutive years and 20 consecutive years.

c. Find the probability which at least 10 funds outperform the market in 5 consecutive years, 10 consecutive years and 20 consecutive years.