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 0.5 0, 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 rst-year policyholder, given that the policyholder reports exactly three claims in a two-year period to the company