In an election, 70% of the voters were Republicans, and 30% were not. Of the Republicans, 60% voted for Candidate X, and of the non-Republicans, 15% voted for Candidate X. Consider a randomly selected voter. Define A = Voter is Republican. B Voted for Candidate X. = (a) Find the values. (Give the answers to two decimal places.) P(A) P(AC) P(BIA) P(B|AC) = = = = (b) Find P(A and B). (Give the answer to three decimal places.) Write in words what outcome it represents. This is the probability of being a non-Republican and voting for Republican. This is the probability of being a non-Republican and voting for Candidate X. This is the probability of being a Republican and voting for Republican. This is the probability of being a Republican and voting for Candidate X. (c) Find P(AC and B). (Give the answer to four decimal places.) Write in words what outcome it represents. This is the probability of being a Republican and voting for Republican. This is the probability of being a non-Republican and voting for Republican. This is the probability of being a Republican and voting for Candidate X. This is the probability of being a non-Republican and voting for Candidate X. (d) Using the results in parts (b) and (c), find P(B). (Give the answer to four decimal places. Hint: The events in parts (b) and (c) cover all of the ways in which B can happen.) (e) Use the result in part (d) to state what percent of the vote Candidate X received. (Give the answer to two decimal places.) %

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