SOA Exam P Sample Question 569
Study guide: Exam P-1
An insurance policy covers a house for ten calendar years for losses due to hailstorm and theft. Only one loss due to hailstorm and only one loss due to theft are covered by the policy during any one calendar year.
For the kth calendar year let H_k be the event that the policy incurs a loss due to hailstorm and let T_k be the event that the policy incurs a loss due to theft. Suppose that the events H_1, \ldots, H_{10}, T_1, \ldots, T_{10} are mutually independent, and that
P[H_k] = 0.2, \quad P[T_k] = 0.1, \quad \text{for all } k.Calculate the probability that the total number of hailstorm and theft losses covered by the policy during the ten calendar years is less than two.
- A)
0.17 - B)
0.23 - C)
0.77 - D)
0.80 - E)
0.83
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