Discussion:
Q: A person claims that she is a fortune teller. Specifically, she claims that she can predict tha 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 predications right now, although that won't affect your answer to the question.) Obviously, you are skeptical, thinking that she is just guessing, so you'll be surprised of 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 4 separate occasions? Answer by assuming that (1) she really is guessing and (2) each day the Dow is equally likely to go up or down.