Hi, this question is another one that I can't seem to arrive at a correct answer on.

Suppose that you're thinking about buying a used R-car at Honest Abe's. In order to make an informed decision you look up the records in an auto magazine and find that 30% of these cars have a faulty transmission. To get more information you hire a mechanic who is excellent: Of all the faulty cars he has examined in the past he correctly judged that 90% were "faulty" and only erroneously judged 10% as "OK." He's almost as good at judging good cars: Of all the good cars he's correctly judged that 80% were "good" and only erroneously judged 20% as "faulty."

What is the probability that the R-car you're thinking of buying has a faulty transmissionif the mechanic judges it to be "faulty"?

a. .72

b. .80

c. .16

d. .66

e. .30

I feel like I'm doing the math as is it was described in the lecture but I'm not coming up with answers that are options in the multiple choice.