Answer: 42.86%

This is a Bayes' theorem problem. Let P(C|M) be the probability of a male having a claim and P(C|F) be the probability of a female having a claim. Given that P(C|F) = 2P(C|M). Using Bayes' theorem: P(M|C) = [P(C|M) * P(M)] / [P(M) * P(C|M) + P(F) * P(C|F)] Given: - P(M) = 0.60 (60% male) - P(F) = 0.40 (40% female) - P(C|F) = 2P(C|M) Substituting: P(M|C) = [P(C|M) * 0.60] / [0.60 * P(C|M) + 0.40 * 2P(C|M)] P(M|C) = [0.60P(C|M)] / [0.60P(C|M) + 0.80P(C|M)] P(M|C) = [0.60P(C|M)] / [1.40P(C|M)] P(M|C) = 0.60 / 1.40 = 0.4286 = 42.86% This shows that even though 60% of policyholders are male, the probability that a claimant is male is only 42.86% because females have twice the probability of making a claim.

Author: Nikitesh Somanthe