Question

Edison Research gathered exit poll results from several sources for the Wisconsin recall election of Scott Walker. They found that 53% of the respondents voted in favor of Scott Walker. Additionally, they estimated that of those who did vote in favor for Scott Walker, 37% had a college degree, while 44% of those who voted against Scott Walker had a college degree.Suppose we randomly sampled a person who participated in the exit poll and found that he had a college degree. What is the probability that he voted in favor of Scott Walker.

Answer 1

Suppose we randomly sampled a person who participated in the exit poll and found that he had a college degree. There is a 48.67% probability that he voted in favor of Scott Walker.

Explanation:

We have these following probabilities:

A 53% probability that a respondent voted in favor of Scott Walker.

A 100%-53%=47% probability that a respondent voted against Scott Walker.

If a respondent voted for Scott Walker, there is a 37% probability that he had a college degree.

If a respondent voted against Scott Walker, there is a 44% probability that he had a college degree.

Suppose we randomly sampled a person who participated in the exit poll and found that he had a college degree. What is the probability that he voted in favor of Scott Walker.

This is the percentage of those who have a college degree and voted for Scott Walker divided by the percentage of those who have a college degree.

Percentage of those who have a college degree.

53% voted for Scott Walker. Of them, 37% have a college degree.

47% voted against Scott Walker. Of them, 44% have a college degree.

So:

`P_(D) = 0.53*(0.37) + 0.47*(0.44) = 0.4029`

Percentage of those who have a college degree and voted for Scott Walker.

53% voted for Scott Walker. Of them, 37% have a college degree.

`P_(DS) = 0.53*0.37 = 0.1961`

So

`P = (P_(DS))/(P_(D)) = (0.1961)/(0.4029) = 0.4867`

Suppose we randomly sampled a person who participated in the exit poll and found that he had a college degree. There is a 48.67% probability that he voted in favor of Scott Walker.