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Sample Actuarial Problems

Apply your math skills to actuarial exam questions.

Actuaries earn professional credentials by passing a series of examinations. This online exam is designed to give you an idea of the types of questions you might encounter on the preliminary actuarial examinations administered by the Casualty Actuarial Society and Society of Actuaries. The sample problems are actual questions from prior exams, but they do not cover all the topics or all levels of difficulty.

Answer the five multiple choice questions below, then click submit to see your results.

1

An insurer offers a health plan to the employees of a large company. As part of this plan, the individual employees may choose exactly two of the supplementary coverages A, B, and C, or they may choose no supplementary coverage. The proportions of the company's employees that choose coverages A, B, and C are 1?4 , 1?3 and 5?12 respectively.

Determine the probability that a randomly chosen employee will choose no supplementary coverage.

2

An insurance company determines that N, the number of claims received in a week, is a random variable with P[N = n] = 1/2n+1, where n > 0 . The company also determines that the number of claims received in a given week is independent of the number of claims received in any other week. Determine the probability that exactly seven claims will be received during a given two week period.

3

A car dealership sells 0, 1, or 2 luxury cars on any day. When selling a car, the dealer also tries to persuade the customer to buy an extended warranty for the car. Let X denote the number of luxury cars sold in a given day, and let Y denote the number of extended warranties sold.
P(X = 0, Y = 0) = 1 / 6
P(X = 1, Y = 0) = 1/12
P(X = 1, Y = 1) = 1 /6
P(X = 2, Y = 0) = 1 /12
P(X = 2, Y = 1) = 1 /3
P(X = 2, Y = 2) = 1/6

What is the variance of X?

4

The stock prices of two companies at the end of any given year are modeled with random variables X and Y that follow a distribution with joint density function

What is the conditional variance of Y given that X = x ?

5

The future lifetimes (in months) of two components of a machine have the following joint density function:

What is the probability that both components are still functioning 20 months from now?