One theory concerning the Dow Jones Industrial Average is that it is likely to increase during U.S. presidential election years. From 1964 through 2008, the Dow Jones Industrial Average increased in 9 of the 12 U.S. presidential election years. Assuming that this indicator is a random event with no predictive value, you would expect that the indicator would be correct 50% of the time.
a. What is the probability of the Dow Jones Industrial Average increasing in 9 or more of the 12 U.S. presidential election years if the probability of an increase in the Dow Jones Industrial Average is 0.50?
b. What is the probability that the Dow Jones Industrial Average will increase in 9 or more of the 12 U.S. presidential election years if the probability of an increase in the Dow Jones Industrial Average in any year is 0.75?