Question

In a certain mid-size city, 90% of the high school graduates are from public schools and the other 10% are from private schools. Of the private school grads, 80% go on to complete college, but only 50% of the public school grads complete college. What is the probability that a person from this city who completes college is a graduate of a private high school?

A. 0.15
B. 0.08
C. 0.10
D. 0.18

Answer 1

Using Bayes' theorem and the law of total probability, we find that there is a 15% chance that a person from this city who completes college is from a private school; answer A is correct.

Step-by-step explanation:

To calculate the probability that a person from this city who completes college is a graduate of a private high school, we use Bayes' theorem. The problem presents us with the following information:

• 90% of high school graduates are from public schools
• 10% are from private schools
• 80% of private school grads complete college
• 50% of public school grads complete college

We are interested in finding P(Private | College), the probability that a person is a private school graduate given that they have completed college. We can calculate it using the formula:

P(Private | College) = P(College | Private) * P(Private) / P(College)

To find P(College), the overall probability that a graduate completes college, we use the law of total probability:

P(College) = P(College | Public) * P(Public) + P(College | Private) * P(Private)

P(College) = 0.50 * 0.90 + 0.80 * 0.10 = 0.45 + 0.08 = 0.53

Now we calculate P(Private | College):

P(Private | College) = 0.80 * 0.10 / 0.53 ≈ 0.15

The correct answer is A. 0.15, which means there is a 15% chance that a college graduate is from a private school.