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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

An insurance company estimates that 40% of policyholders who have only an auto policy will renew next year and 60% of policyholders who have only a homeowners policy will renew next year. The company estimates that 80% of policyholders who have both an auto and a homeowners policy will renew at least one of those policies next year.

Company records show that 65% of policyholders have an auto policy, 50% of policyholders have a homeowners policy, and 15% of policyholders have both an auto and a homeowners policy.

Using the company's estimates, calculate the percentage of policyholders that will renew at least one policy next year.

2

An actuary studying the insurance preferences of automobile owners makes the following conclusions:

  1. An automobile owner is twice as likely to purchase collision coverage as disability coverage.
  2. The event that an automobile owner purchases collision coverage is independent of the event that he or she purchases disability coverage.
  3. The probability that an automobile owner purchases both collision and disability coverages is 0.15.

What is the probability that an automobile owner purchases neither collision nor disability coverage?

3

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.

4

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.

5

A company takes out an insurance policy to cover accidents that occur at its manufacturing plant. The probability that one or more accidents will occur during any given month is 3/5.

The number of accidents that occur in any given month is independent of the number of accidents that occur in all other months.

Calculate the probability that there will be at least four months in which no accidents occur before the fourth month in which at least one accident occurs.