In an election, 66% of the voters were Republicans, and 34% were not. Of the Republicans, 60% 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) Find the values. P(A) = P(AC) = P(B|A) = P(B|AC) = (b) Find P(A and B). Write in words what outcome it represents. This is the probability of being a non-Republican and voting for a Republican.This is the probability of being a Republican and voting for Candidate X. This is the probability of being a Republican and voting for a Republican.This is the probability of being a non-Republican and voting for Candidate X. (c) Find P(AC and B). Write in words what outcome it represents. This is the probability of being a Republican and voting for Candidate X.This is the probability of being a Republican and voting for a Republican. This is the probability of being a non-Republican and voting for Candidate X.This is the probability of being a non-Republican and voting for a Republican. (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.

Question

In an election, 66% of the voters were Republicans, and 34% were not. Of the Republicans, 60% 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)

Find the values.

P(A) = P(A^C) = P(B|A) = P(B|A^C) =

(b)

Find P(A and B).

Write in words what outcome it represents.

This is the probability of being a non-Republican and voting for a Republican.This is the probability of being a Republican and voting for Candidate X. This is the probability of being a Republican and voting for a Republican.This is the probability of being a non-Republican and voting for Candidate X.

(c)

Find P(A^C and B).

Write in words what outcome it represents.

This is the probability of being a Republican and voting for Candidate X.This is the probability of being a Republican and voting for a Republican. This is the probability of being a non-Republican and voting for Candidate X.This is the probability of being a non-Republican and voting for a Republican.

(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.