Probability - probability tree
6. I am thinking about buying a used car. To make an informed decision, I look up the records of used cars in an auto magazine, and find that, unfortunately, 30% have defective transmissions. To get more information on the particular used car, I hire a mechanic who can make a guess on the basis of a quick drive around the block. Of course, he isn't always right; but he does have an excellent record: Of all the faulty cars he has examined in the past he correctly pronounced 90% "defective"; in other words, he wrongly pronounced only 10% "OK." He has almost as good a record in judging good cars: He has correctly pronounced 80% "OK," while he wrongly pronounced only 20% "defective." (Please note that "defective" in quotation marks describes the mechanic's opinion, while defective with no quotation marks describes the actual state of the car.)
What is the probability that the used car I am thinking of buying has a defective transmission in the following three cases:
a. Before I hire the mechanic?
b. After I hire the mechanic and given that he pronounces the used car "defective"?
c. After I hire the mechanic and given that he pronounces the used car "OK"?
(Hint: Draw a probability tree diagram for the question first.)
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