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**Problem 24A**

An insurance portfolio consists of four policyholders. The number of claims for each policyholder in a calendar year follows a distribution with the following probability function:

Assume that the number of claims for one policyholder is independent of the number of claims for any one of the other policyholders in the portfolio. What is the probability that the total number of claims in this portfolio in the upcoming calendar year is 4?

**Problem 24B**

Use the same information as in Problem 24A. What is the probability that there will be at most 4 claims in the portfolio in the upcoming year?

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**Answers**

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I love your problems and I greatly appreciate it that you have this website available to the public. I wonder if you charge for people to see the actual solutions, I’d love to purchase the solutions for these problems. I’m having a difficult time solving some of these problems and your answer keys do not have enough information for me to understand them. Thank you so much. I’m looking forward to your reply.

The blog is meant to be a free resource for anyone who wants to take exam P. It is one of my future projects to post worked solutions to the problems (at least some outline sketches). I haven’t been able to find the time. Until then, you can just leave comments or questions at any problem that you have difficulty with. I will try to review questions as best I can.

Dan Ma