Question

2.24 Exit poll: Edison Research gathered exit poll results from several sources for the Wisconsin recall election of Scott Walker. They found that 55% of the respondents voted in favor of Scott Walker. Additionally, they estimated that of those who did vote in favor for Scott Walker, 32% had a college degree, while 47% 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?

(please round to 4 decimal places)

Answer 1

So the probability that the person who has a college degree voted in favor of Scott Walker is 0.4433 (rounded to 4 decimal places).

Explanation:

Let A be the event that the person voted in favor of Scott Walker, and let B be the event that the person has a college degree. We want to find P(A|B), the probability that the person voted in favor of Scott Walker given that they have a college degree.

Using Bayes' theorem, we have:

P(A|B) = P(B|A) * P(A) / P(B)

We know that P(A) = 0.55, the proportion of people who voted in favor of Scott Walker. We also know that P(B|A) = 0.32, the proportion of people who voted in favor of Scott Walker and have a college degree.

To find P(B), the proportion of people with a college degree, we need to use the law of total probability:

P(B) = P(B|A) * P(A) + P(B|not A) * P(not A)

We know that P(B|not A) = 0.47, the proportion of people who voted against Scott Walker and have a college degree. We also know that P(not A) = 1 - P(A) = 0.45, the proportion of people who did not vote in favor of Scott Walker.

Therefore, we have:

P(B) = 0.32 * 0.55 + 0.47 * 0.45 = 0.3965

Now we can substitute these values into Bayes' theorem:

P(A|B) = 0.32 * 0.55 / 0.3965 = 0.4433