A large group of voters in two nearby counties were surveyed about which political party they prefer between parties X, Y, and Z. The relative frequencies in the table below summarize the results of the survey.
a. If one surveyed person is selected at random:
i. What is the probability that the person lives in County A and prefers Party Z?
ii. What is the probability that the person lives in County A or prefers Party Z?
iii. What is the probability that the person lives in County A, given that they prefer Party Z?
b. In the survey, are the events “Lives in County B” and “Prefers Party X” independent? Explain why or why not.
c. Assume that the distribution of party preference shown in the table holds true in the entire state. If 5 voters from the state are selected at random, what is the probability that exactly 2 of them prefer Party Y?