# Exam P Practice Problem 24 – Total Number of Claims

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Problem 24A
An insurance portfolio consists of four policyholders. The number of claims $N$ for each policyholder in a calendar year follows a distribution with the following probability function:

$\displaystyle P(N=k)=\biggl( \frac{13}{25} \biggr)^k \ \frac{12}{25} \ \ \ \ \ \ \ \ k=0,1,2,3,\cdots$

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?

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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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