Suppose an insurance company classifies a “serious” flood as one where at least one home that they insure is destroyed by the flood. Let Y denote the number of homes that they insure that are destroyed by a serious flood in the southern United States. The pmf for Y can be modeled by a Poisson distribution with mean 14 homes. Because of the high risk of floods in the area (and therefore cost to the customers), the insurance company offers basic and premium policies. The basic policy does not cover damage from floods, while the premium policy does. 67% of policy holders opt for the premium coverage. We will assume that flood occurrence and policyholders are independent of each other. What is the probability that five or fewer homes, that the company insures, will be destroyed by a serious flood in the southern United States? Suppose a serious flood destroys 21 homes that the company insures. What is the probability that at least 15 of those homes were premium policyholders?

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