Reference no: EM132846862

You are the Claims Manager for a small auto insurance firm. You know the following facts: - 20% of your policy-holders are younger (age 16-34). Within this group, 60% are men and 40% are women. The men have a 10% probability of making a claim, while the women have a 5% probability of making a claim. - 60% of your policy-holders are middle-aged (ages 35-59). Of these, 50% are men and 50% are women. The men and women within this age group have 4% and 3% probabilities of making a claim, respectively. - 20% of your policy-holders are older (ages 60 and above). Of these, 55% are women and 45% are men. The men and women each have a 3% probability of making a claim. - Any claim will cost the firm $20,000.

(a) For any randomly-selected claim, what is the probability that the claimant is younger? Middle-aged? Older?

(b) For any randomly-selected claim, what is the probability that the claimant is male? Female?

(c) What is the expected claim amount per policy-holder?