Question

In the 2012 presidential election, exit polls from the critical state of Ohio provided the following results:

Obama Romney No college degree (60%) 52% 45% College graduate (40%) 47% 51%
If a randomly selected respondent voted for Obama, what is the probability that the person has a college degree?

Answer 1

If a randomly selected respondent voted for Obama, there is a 37.6% probability that the person has a college degree.

Explanation:

We have these following probabilities:

A 60% probability that a randomly selected respondent voted is not a college graduate

A 40% probability that a randomly selected respondent is a college graduate

If the randomly selected respondent is not a college graduate, there is a 52% probability that he voted for Obama and a 45% probability that he voted for Romney.

If the randomly selected respondent is a college graduate, there is a 47% probability that he voted for Obama and a 51% probability that he voted for Romney.

If a randomly selected respondent voted for Obama, what is the probability that the person has a college degree?

This is the probability that a person has a college degree and voted for Obama divided by the probability that a person voted for Obama. So

College graduated and voted for Obama

40% are college graduates.

Of them, 47% voted for Obama.

So

`0.4*0.47 = 0.188`

0.188 probability that a person is a college graduate and voted for Obama

Voted for Obama

60% are not college graduates

Of them, 52% voted for Obama

40% are college graduates.

Of them, 47% voted for Obama.

So

`0.6*0.52 + 0.4*0.47 = 0.5`

Final probability

`P = (0.188)/(0.5) = 0.376`

If a randomly selected respondent voted for Obama, there is a 37.6% probability that the person has a college degree.