# What is the best way to study for Exam P?

According to the previous post called Probability and Actuarial Science, actuaries are specially-trained professionals who use their knowledge of probability, statistics, and specific models to evaluate and price risks, e.g. risks of living too long, the risks of dying too soon, the risks of property damages, the risks of becoming sick and a whole host of other risks that are quantifiable. To be an actuary, a candidate must pass a series of exams.

It is fitting that the first actuarial exam, called Exam P, is on probability. How hard is Exam P? What is the pass rate? How much time should a student spend in studying for Exam P?

Exam P is administered by the Society of Actuaries (SOA). It is a 3-hour multiple choice exam consisting of 30 questions. There is a rule of thumb that says that the number of hours required for studying an actuarial exam is the length of the exam times 100. This would mean Exam P may requires 300 hours of studying and preparation.

The 300-hour requirement is not far fetched. Typically a student should take an undergraduate course in probability and statistics (calculus based) prior to taking Exam P. The class time for such as course can certainly be a part of the 300 hours.

Let’s say the class time is around 90 hours (spread over two 15-week semesters with 3 hours of class time each week). That leaves 210 hours for a period of intense studying prior to taking Exam P, sometime after taking the probability and stats course.

In fact, the most effective form of studying is working practice problems. In these 210 hours, the student should review concepts for sure. However, the best way to review is to apply what he or she has learned in the probability and stats course through problem solving.

Intense problem solving is not optional as the pass rate for Exam P and other actuarial exams tend to be around 40%. If a student spends 15 hours a week studying, the 210 hours of studying would take about 3 and a half months. Passing actuarial exams requires dedication.

We give another plug for our Exam P site. It has over 100 realistic Exam P practice problems. We know of students who passed Exam P as a result of studying our practice problems.

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# Probability and actuarial science

Consider this scenario. Both a thirty-year old man and a seventy-year old man purchase identical annuity contracts. The costs of the contracts are the same to both men. The benefits are also the same – both men receive the same monthly payment till death. What is wrong with this picture?

The life expectancy of a thirty-year old is four times longer than that of a seventy-year old. So such an annuity contract would be a good deal for the thirty-year old as he can stand to collect four times more payments than a seventy-year old (but with time value of money the differential is more than 4 times).

Such contracts sold to a thrity-year old would be a bad deal for the insurance company. In fact if the insurance company had sold such contracts to a sufficient number of thirty-year old, it almost certainly would go out of business long before the thirty-year old can live to an old age. Though good deal for the young folks, such practices are simply not sustainable both as a business practice and as a matter of public policy.

Yet back in the seventeenth century, during the reign of William III of England, this was what commonly happened – annuity contracts with the same prices and the same payouts were routinely sold to both thirty-year old and seventy-year old (see Karl Pearson, The History of Statistics In the 17th and 18th Centuries against the Changing Background of Intellectual, Scientific and Religious Thought).

Why? People back in those days did not have any conceptualization of probability or statistics. For example, they did not know that the length of someone’s life, though unpredictable on an individual basis, could be predicted statistically based on empirical observations over time and across a large group of people. The prevailing mentality was that God controlled every minute detail of the universe. Such belief ruled out any kind of conceptualization of chance as phenomena that can be studied and predicted in the aggregate.

Fast forward to the present. We now take probability seriously (and the seriousness had been steadily growing since the eighteenth century). Probability tools are widely available. Here’s a life expectancy calculator from Social Security. According to this calculator, the additional life expectancy of a man who is currently thirty-year old is 51.4 years. A man who is currently seventy-year old is expected to live 14.8 more years. So a thirty-year old man can expect to live three and a half times longer than a seventy-year old man.

With a strong foundation of probability and statistics, which was not available in the seventeenth century, annuity contracts are priced based on the probability of living a long life and the life insurance policies are priced based on the probability of dying prematurely.

Actuaries are specially-trained professionals who use their knowledge of probability, statistics, and specific models to evaluate and price risks, e.g. risks of living too long, the risks of dying too soon, the risks of property damages, the risks of becoming sick and a whole host of other risks that are quantifiable. As a result, actuaries are generally employed in life, health, and property and casualty insurance companies, consulting firms, and government.

In fact the actuarial profession grew out of the effort to put the pricing of life insurance and annuity contracts on a sound scientific and business basis in the early eighteenth century England.

The entry point into the actuarial profession is an exam on probability. It is called Exam P and is jointly administered by the Society of Actuaries (SOA) and the Casualty Actuarial Society (CAS). Here’s what SOA says about Exam P:

The purpose of the syllabus for this examination is to develop knowledge of the fundamental probability tools for quantitatively assessing risk. The application of these tools to problems encountered in actuarial science is emphasized. A thorough command of the supporting calculus is assumed. Additionally, a very basic knowledge of insurance and risk management is assumed.

In its current incarnation, it is a three-hour exam that consists of 30 multiple-choice questions and is administered as a computer-based test.

To be an actuary, a candidate must pass a series of exams (see here for the exam requirements from SOA). Exam P is the first of many exams. It is not surprising that Exam P is the first exam since the probability is part of the foundation of actuarial science.

How difficult is Exam P? The pass rates are typically low. Exam P is administered six times a year at test locations throughout the country. Less than 45% of the candidates earn a passing score. Often times, the pass rates dip below 40%.

Exam P is an entry point of of the actuarial exam system. It is the first of many exams in the pathway to becoming an actuary. We have a companion blog for studying Exam P.

This blog has viewership on a daily basis from every continent. In fact, some aspiring actuaries passed Exam P as a result of using this blog. Here’s two practice problems.

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$\copyright$ 2017 – Dan Ma