Question: A woman claims that she is a fortune-teller. Specifically, she claims that she can predict the direction of the change (up or down) in the Dow Jones Industrial Average for the next 10 days (such as U, U, D, U, D, U, U, D, D, D). (You can assume that she makes all 10 predictions right now, although that does not affect your answer to the question.) Obviously, you are skeptical, thinking that she is just guessing, so you would be surprised if her predictions are accurate. Which would surprise you more:
(1) she predicts at least 8 out of 10 correctly, or
(2) she predicts at least 6 out of 10 correctly on each of four separate occasions?
Answer by assuming that (1) she is really guessing and (2) each day the Dow is equally likely to go up or down.