a) There are two car factories, A and B. Each year, factory A produces 1000 cars, of which 10 are lemons. Factory B produces 2 cars, each of which is a lemon. All cars go to a single lot. where they are thoroughly mixed up. I buy a car. (Marks: 10) - What is the probability it is a lemon? - What is the probability it came from factory B? . The car is now revealed to be a lemon. What is the probability it came from factory B, conditioned on the fact it is a lemon? b) Disease A occurs with probability 0.1 (i.e., it is present in 10% of the population), and disease B occurs with probability 0.2. It is not possible to have both diseases. You have a single test. This test reports positive with probability 0.8 for a patient with disease A, with probability 0.5 for a patient with disease B, and with probability 0.01 for a patient with no disease. What is the posterior probability you have either disease, or neither, if the test comes back positive