**Problem 18-A**

A portfolio of independent risks is divided into five distinct classes that are equal in size.

The annual claim count distribution for any risk in this portfolio is assumed to be a binomial distribution. The following table shows more information about these five classes.

A risk is randomly selected from this portfolio and is observed to have one claim in the last year.

What is the probability that the mean number of claims in a year for this risk is greater than 1.5?

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**Problem 18-B**

A portfolio of independent risks is divided into five distinct classes that are equal in size.

The annual claim count distribution for any risk in this portfolio is assumed to be a geometric distribution. The following table shows more information about these five classes.

A risk is randomly selected from this portfolio and is observed to have one claim in the last year.

What is the probability that the mean number of claims in a year for this risk is greater than 2.5?

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Tagged: Actuarial Exam, Bayesian Credibility, Bayesian Probability, Binomial Distribution, CAS Exam 4, CAS Exam 4 Practice Problem, Frequency, Geometric Distribution, Loss Models, Mixture Distribution, Posterior Distribution, Prior Distribution, Probability, SOA Exam C, SOA Exam C Practice Problem, Variance

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