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 grades complete college.

What is the probability that a person from this city who completes college is a graduate of a private high school? Show your work.

A: 0.8

B: 0.15

C: 0.10

D: 0.80

E: 0.18