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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.


You are given

Determine P[A] .


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?


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.


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 ?


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?