1 I. An insurance company hires an actuary to calculate the probability that an automobile policyholder files more than one claim during three-year period. The actuary takes the following steps. (a) He uses pn to represent the probability that the policyholder files n claims during the period. He also makes the simplifying assumption that for all integers n 2 0, pn 0.2pm-1. Explain the meaning of the assumption using plain language. (b) Express p,P2>Ps in terms of po. Do you recognize a pattern? Express pn in terms of po. (c) The sum of all probabilities is always 1. Here n is a discrete variable, so a series can be used to express the sum of all probabilities. Write down this series, then find po- (d) Use a series to express the possibility that one policyholder files more than one claim and then find this possibility