試題詳解

85. Under an insurance policy, a maximum of five claims may be filed per year by a policyholder. Let p n( ) be the probability that a policyholder files n claims during a given year, where n = 0,1,2,3,4,5. An actuary makes the following observations:
i) p(n)≥p(n+1) for n=0, 1, 2, 3, 4 .
ii) The difference between p (n) and p (n+1) is the same for n = 0,1,2,3,4.
iii) Exactly 40% of policyholders file fewer than two claims during a given year.
Calculate the probability that a random policyholder will file more than three claims during a given year.
(A) 0.14
(B) 0.16
(C) 0.27
(D) 0.29
(E) 0.33