SOA Exam P Sample Question 85
Study guide: Exam P-1
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) \ge 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
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