Respuesta :
Answer:
If a randomly selected respondent voted for Obama, there is a 37.6% probability that the person has a college degree.
Step-by-step 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
[tex]0.4*0.47 = 0.188[/tex]
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
[tex]0.6*0.52 + 0.4*0.47 = 0.5[/tex]
Final probability
[tex]P = \frac{0.188}{0.5} = 0.376[/tex]
If a randomly selected respondent voted for Obama, there is a 37.6% probability that the person has a college degree.
