An insurance company will insure a modest house for $500,000 against complete destruction from fire for a premium of $700 a year. Suppose that the probability that the house will be destroyed by fire in a given year is .0005. Let X denotes the annual profit of the insurance profit.

a) Give the probability distribution of the profit X in the tabular form.
b) Calculate the insurance company’s expected profit.
c) Find the annual premium that the company should charge if it wants its expected
profit to be $600.

Question

An insurance company will insure a modest house for $500,000 against complete destruction from fire for a premium of $700 a year. Suppose that the probability that the house will be destroyed by fire in a given year is .0005. Let X denotes the annual profit of the insurance profit.

a) Give the probability distribution of the profit X in the tabular form.
b) Calculate the insurance company’s expected profit.
c) Find the annual premium that the company should charge if it wants its expected
profit to be $600.