Question 16 In modeling the number of claims filed by an individual under an automobile policy during a three-year period, an actuary makes the simplifying assumption that for all integers n 20, p(n + 1) = 0.2p(n) where p(n) represents the probability that the policyholder files exactly n claims during the period. Under this assumption, calculate the probability that a policyholder files more than one claim during the period. Hint: Show that for all integer n 2 0, p(n) = (0.2)" p(0) and the obvious fact that _p(n) = 1. n=0