Prior to presidential elections citizens of voting age are surveyed. In the population, two characteristics of voters are their registered party affiliation (republican, democrat, or independent) and for whom they voted in the previous presidential election (republican or democrat). Let us draw a citizen at random, defining these two variables.

a. Suppose that the probability of drawing a person who voted republication in the last election is 0.466 , and the probability of drawing a person who is registered republican is 0.32 , and the probability that a randomly selected person votes republican given that they are a registered republican is 0.97 . Compute the joint probability \(\operatorname{Prob}[P A R T Y=-1, V O T E=-1]\). Show your work.

b. Are these random variables statistically independent? Explain.

Transcribed Image Text:

-1 registered republican PARTY=0 0 independent or unregistered 1 -1 VOTE= = 1 registered democrat voted republican in previous election voted democratic in previous election