An insurance company's records of 12,299 automobile insurance policies showed that 2073 policy holders made a claim (Courtesy J. Hickman). Among insured drivers under age 25, there were 1032 claims out of 5192 policies. For person selected at random from the policy holders, let \(A=\) [Claim was filed] and \(B=[\) Under age 25] .

(a) Fill in the four probabilities, and the marginal totals, in the table

(b) Use Bayes' Theorem to obtain the probability that the person is under age 25 given that a claim was filed.

(c) Check your answer using directly from your table in Part (a) and the definition of \(P(B \mid A)\).

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A B