In a recent election, 55% of the voters were Republicans, and 45% were not. Of the Republicans, 80% voted for Candidate X, and of the non-Republicans, 10% voted for Candidate X. Consider a randomly selected voter. Define
A = Voter is Republican.
B = Voted for Candidate X.
a. Write values for P(A), P(AC), P(B|A), and P(B|AC).
b. Find P(A and B), and write in words what outcome it represents.
c. Find P(AC and B), and write in words what outcome it represents.
d. Using the results in parts (b) and (c), find P(B). (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.