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Bayesian Probability

Yearly anutomobile inspections are required for residents of the state of Pennsylvania.Suppose that 18% of all inspected cars in Pennsylvania have problems that need to be corrected. Unfortunately, pennsylvania state inspections fail to detect these problems 12% of the time. On the other hand, an inspection never detects a problem when there is no problem. Consider a car that is inspected and is found to be free of problems. What is the probability that there is indeed something wrong that the inspection has failed to uncover?

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Probability that car has a problem = 18%

Probability that a problem ...