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Solve Real 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

You are given

Determine P[A] .

2

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.

3

A device runs until either of two components fails, at which point the device stops running.  The joint density function of the lifetimes of the two components, both measured in hours, is 

f (x,y)=x+y/8 for 0< x < 2 and 0< y < 2 .

What is the probability that the device fails during its first hour of operation?

4

Let T1 be the time between a car accident and reporting a claim to the insurance company. Let T2 be the time between the report of the claim and payment of the claim. The joint density function of T1 and T2, f(t1, t2), is constant over the region 0 < t1 < 6, 0< t2 < 6, t1 + t2 < 10, and zero otherwise. Determine E[T1 + T2], the expected time between a car accident and payment of the claim.

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?