Many investors are prone to listening to “stock pickers” who claim to have beaten the stock market on a consistent basis. Most academics, however, are convinced that the stock market is generally random. Assume that there are only two possible outcomes for the stock market on any given day: Outcome A—the market will go up; or Outcome B—the market will go down. Assume further that the two outcomes are equally likely each day and that daily market performances are statistically independent.
a. What is the likelihood the market will have fve consecutive winning days?
b. Suppose on each of the fve days 1000 stock pickers just flip a coin to decide whether the market will go up or go down that day. How many of them would we expect to be right on all five days?