CS1 - Practice Questions
- anactuary1729
- Dec 17, 2023
- 1 min read
1. A large portfolio consists of 20% class A policies, 50% class B policies, and 30% class C policies. Ten policies are selected at random from the portfolio.
(i) Calculate the probability that there are no policies of class A among the randomly selected ten. [1]
(ii) (a) Calculate the expected number of class B policies among the randomly selected ten.
(b) Calculate the probability that there are more than five class B policies among the randomly selected ten. [2]
[Total 3]
2. Consider six life policies, each on one of six independent lives. Each of four of the policies has a probability of 2/3 of giving rise to a claim within the next five years, and each of the other two policies has a probability of 1/3 of giving rise to a claim within the next five years. It is assumed that only one claim can arise from each policy.
(i) Calculate the expected number of claims which will arise from the six policies within the next five years. [2]
(ii) Calculate the probability that exactly one claim will arise from the six policies within the next five years. [2]
(iii) Calculate the probability that two policies chosen at random from the six policies will both give rise to claims within the next five years. [4]
[Total 8]
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