Chapter 5, Problem 36PS

One theory concerning the Dow jones industrial Average is that it is likely to increase during U.S. presidential election years. For 1964 through 2016, the Dow jones industrial Average increased in 11 of U.S. Presidential election years. Assuming that this indicator is a random with no predictive value, you would expect that indicator would be correct $50\%$ of the time.

a. What is the probability of the Dow Jones Industrial Average increasing in 11 or more of the 14 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 11 or more of the 14 U.S. Presidential election years if the probability of an increase in the Dow Jones Industrial Average in any year is $0.75?$