試題詳解

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