Financial Risk Manager Part 1
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60% of an insurer's policyholders are male and 40% are female. The chance of a female having a claim is twice the chance of a male having a claim. Given a randomly selected policyholder has a claim, what's the probability he is a male?
Other
Community
NNikitesh
A
60%
B
65%
C
70%
D
42.86%
Explanation:
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.
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