SOA Exam P Sample Question 187
Study guide: Exam P-1
An actuary has done an analysis of all policies that cover two cars. 70% of the policies are of type A for both cars, and 30% of the policies are of type B for both cars. The number of claims on different cars across all policies are mutually independent. The distributions of the number of claims on a car are given in the following table.
| Number of Claims | Type A | Type B |
|---|---|---|
| 0 | 40% | 25% |
| 1 | 30% | 25% |
| 2 | 20% | 25% |
| 3 | 10% | 25% |
Four policies are selected at random.
Calculate the probability that exactly one of the four policies has the same number of claims on both covered cars.
- A) 0.104
- B) 0.250
- C) 0.285
- D) 0.417
- E) 0.739
Answer this question and see the worked solution