Suppose an automobile insurance company classifies a driver as good, average, or bad. Of all their insured drivers, 25% are classified good, 50% are average, and 25% are bad. Sup- pose for the coming year, a good driver has a 5% chance of having an accident, and aver- age driver has 15% chance of having an accident, and a bad driver has a 25% chance. If you had an accident in the past year what is the probability that you are a good driver?

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