# Exam P Practice Problem 20 – Poisson Number of Claims

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Problem 20A
Ten percent of the policyholders for an auto insurance company are considered high risk and ninety percent of its policyholders are considered low risk. The number of claims made by a policyholder in a calendar year follows a Poisson distribution with mean $\lambda$.

For high risk policyholders, $\lambda=0.9$. For low risk policyholders, $\lambda=0.1$. An actuary selects one policyholder at random. What is the probability that this policyholder will have at least 1 claim in the upcoming calendar year?

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Problem 20B
Use the same information as in Problem 20A. Given that the randomly selected policyholder has at least one claim, what is the probability he or she has more than 1 claim?

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