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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

A survey of a group's viewing habits over the last year revealed the following information:

  1. 28% watched gymnastics
  2. 29% watched baseball
  3. 19% watched soccer
  4. 14% watched gymnastics and baseball
  5. 12% watched baseball and soccer
  6. 10% watched gymnastics and soccer
  7. 8% watched all three sports.

Calculate the percentage of the group that watched none of the three sports during the last year.

2

You are given

Determine P[A] .

3

A blood test indicates the presence of a particular disease 95% of the time when the disease is actually present. The same test indicates the presence of the disease 0.5% of the time when the disease is not present. One percent of the population actually has the disease. Calculate the probability that a person has the disease given that the test indicates the presence of the disease.

4

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?

5

An insurance company issues life insurance policies in three separate categories: standard, preferred, and ultra-preferred. Of the company’s policyholders, 50% are standard, 40% are preferred, and 10% are ultra-preferred. Each standard policyholder has probability 0.010 of dying in the next year, each preferred policyholder has probability 0.005 of dying in the next year, and each ultra-preferred policyholder has probability 0.001 of dying in the next year.

A policyholder dies in the next year.

What is the probability that the deceased policyholder was ultra-preferred?