An automobile insurance company has determined the accident rate (probability of having at least one accident during a year) for various age groups. (See Table 2.) Suppose that a policyholder calls in to report an accident. What is the probability that they are over 60?
Table

Use Bayes' theorem to calculate the probabilities?

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Proportion of Total Insured Age Group Accident Rate .05 Under 21 .06 .04 21-30 .10 31-40 .25 .02 41-50 20 .015 51-60 .30 .025 Over 60 .10 .04