314. An auto insurance company tracks the experience of its first-year and multi-year
policyholders separately. First-year policyholders account for 15% of the company's
business while multi-year policyholders account for the rest.
The number of claims reported to the company in a year by a first-year policyholder
follows a Poisson distribution with mean 0.50, while the number of claims reported to the
company in a year by a multi-year policyholder follows a Poisson distribution with mean 0.20.
Calculate the probability that a policyholder is a first-year policyholder, given that the
policyholder reports at least one claim in a year to the company.
(A) 0.246
(B) 0.277
(C) 0.306
(D) 0.476
(E) 0.685
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