Problem 3 Suppose that of all used cars of a particular year, make, and model, 5

Question

Problem 3

Suppose that of all used cars of a particular year, make, and model, 50% have bad brakes. You are considering buying a used car of this year, make, and model. You take the car to a mechanic to have the brakes checked. The mechanic is not infallible: the chance that the mechanic will correctly report that a car with bad brakes has bad brakes is 40%, and the chance that the mechanic will erroneously report that a car with good brakes has bad brakes is 10%. Assuming that the car you take to the mechanic is selected "at random" from the population of cars of that year, make, and model, the chance that the car's brakes are good given that the mechanic says its brakes are good is

Explanation / Answer

P(mechanic says its brakes are good)=P(good breaks and breaks are good+bad breaks and breaks are good)

=0.5*0.6+0.5*0.9=0.75

hence P(good breaks|mechanic says its brakes are good)=0.5*0.9/0.75=0.6

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