SOA Exam P: Probability for Actuaries Part 1 (Actuarial)

Name: SOA Exam P: Probability for Actuaries Part 1 (Actuarial)
Rating: 4.7 (395 reviews)

This course, along with Part 2 and Part 3, provide the necessary skills and knowledge to pass SOA Exam P and CAS Exam 1

Created byClayton Zaluski

Last updated 7/2025

English

English [Auto],

What you'll learn

Probability
SOA Exam P and CAS Exam 1
Probability for Actuaries
Statistics
Actuarial Science
Random Variables
Discrete Distributions
Continuous Distributions

Course content

3 sections • 19 lectures • 5h 51m total length

Probability for Actuaries: Part 1 - Introduction3:14
Explore introductory probability concepts for actuaries, including set theory, probability spaces, counting methods, conditional probability, and random variables across discrete, continuous, and mixed types.
Study Manual Download0:09
Online Resources0:02

Set Theory10:11
Explore set theory foundations for probability by defining sets and elements, notation, null sets, and subsets. Learn unions, intersections, complements, and mutual exclusivity with clear examples.
Sample Spaces (or Probability Spaces) and Venn Diagrams20:56
Explore sample spaces and Venn diagrams, learn sample points, complements, unions and intersections, and apply these concepts through practical probability examples.
Basic Probability Models27:05
Learn basic probability models and core concepts, including axioms, union and intersection, DeMorgan's laws, and real-world examples with dice and Venn diagrams.
Counting Problems, Permutations and Combinations37:51
Learn counting methods using factorials, permutations, and combinations to solve lineups, license plates, card selections, and probability problems with clear step-by-step examples.
Conditional Probability22:45
Learn conditional probability by computing the probability of A given B as the ratio of A intersect B to B, using Venn diagrams and key rules.
Independent Events16:47
This lecture defines independent events, shows how intersection, union, and conditional probabilities relate, and demonstrates independence with X, Y, Z and insurance examples, including complements.
Bayes' Rule and Total Law of Probability32:47
Apply the total probability law and Bayes' rule to compute conditional probabilities across insurance risk, hospital outcomes, age-based accident risk, and grade pass rates.

Introduction to Random Variables2:22
Explore the concept of a random variable, its mapping of random outcomes to real numbers, and the distinction between discrete and continuous variables with sums and integrals.
Discrete Random Variables34:07
Learn how discrete random variables work, define the PMF and CDF, and solve real examples—from sums of two dice to insurance-claim models using recursion and conditional probability.
Continuous Random Variables12:45
Explore continuous random variables, their probability density function (pdf) and cumulative distribution function (cdf), and compute probabilities via area under the curve and derivatives, noting zero point mass.
Survival Functions and Hazard Rates3:57
Define survival functions and hazard rates, S(X)=1-F(X), compute the CDF from the given pdf, and evaluate the survival at x=0.6.
Expected Values and Other Statistics50:38
Explore expected values and moments for discrete and continuous distributions, including the mean (first moment), second moment, variance, standard deviation, skewness, and kurtosis, with practical actuarial examples.
Percentiles, Median and Mode17:37
Master percentiles, the median, and the mode in probability for actuaries, with practical examples using density functions and CDFs.
Mixed Distributions26:09
Explore mixed distributions, combining discrete and continuous parts, with probability mass and density functions, and learn to compute probabilities, moments, and endpoint masses.
Moment Generating Functions23:18
Master moment generating functions to extract moments like the mean and variance by derivatives at zero. Apply MGFs to sums and linear transformations in actuarial examples.
Probability Generating Functions9:03
Explore probability generating functions for discrete random variables, derive probabilities using derivatives at zero, and compute the mean from the first derivative evaluated at one, with MGF relations.

Requirements

Basic knowledge of introductory statistics, calculus (differentiation, limits, integrals), algebra

Description

Are you studying for your first actuarial exam? Do you want to one day work as an Actuary, which is consistently ranked as a top 10 career?

Well then, you’ve come to the right place!

This is where you start. And it is the perfect time to start. Actuaries are in high demand globally. Actuaries can earn a great living and enjoy great job satisfaction.

To become a fully qualified actuary, you have to pass a series of professional exams. Most students start by taking a related university degree. This course along with Part 2 and Part 3 to the course, will provide you with the skills required to pass the first actuarial exam.

Whether you are writing with the Society of Actuaries (SOA) or Casualty Actuarial Society (CAS), this course is for you. The material for SOA Exam P or CAS Exam 1 is covered in this course and Part 2 and Part 3 to this course.

Part 1 will cover the following areas of the exam:

Set Theory, Sample Spaces and Probability Spaces
Basic Probability Theory
Counting Problems, Permutations and Combinations
Conditional Probability and Independent Events
Bayes' Rule and the Total Law of Probability
Discrete and Continuous Random Variables
Probability Density Function (PDF), Cumulative Distribution Function (CDF) and Survival Functions
Expected Values, Higher Moments, Variance, Standard Deviation and Coefficient of Variation
Percentiles, Median and Mode
Mixed Distributions
Moment Generating Functions (MGFs) and Probability Generating Functions (PGFs)

Practice makes perfect with actuarial exams. As such, we have included many practice problems for you to hone your skills. The SOA also provides sample questions and we highly recommend that you practice your skills on these questions as well.

Teaching is my passion!

I have been teaching actuaries around the world since 2014 and have helped 100s of actuaries pass actuarial exams. I have also taught at the University level, teaching courses on probability and mathematical statistics. My teaching style focuses on explaining concepts and then illustrating those concepts with lots of examples. I find that this allows the students to understand the basics and then directly tie the theory to practical applications with practice problems. This sets the students up for success with the actuarial exams that they intend to write.

Why take this course?

This course (along with Part 2 and Part 3) is designed to cover the SOA Exam P/CAS Exam 1 syllabus in entirety. This course is specifically tailored to the actuarial exam. There are a lot of other courses that teach probability and statistics, however, they are more general in nature, whereas this course focuses exclusively on getting you to a passing grade come exam day. My course also offers you lifetime access to the material and was priced at a price point that would be affordable to students around the world.

What you get with this course?

You get access to over 17 hours of video lectures that cover the entire syllabus, split between Part 1, Part 2 and Part 3. You also get access to an electronic manual for the course and over 100 practice questions to hone your skills and prepare you for the actual exam day.

Who this course is for:

Actuarial Students
Statistics Students
Mathematics Students

SOA Exam P: Probability for Actuaries Part 1 (Actuarial)

What you'll learn

Explore related topics

Course content

Probability for Actuaries: Part 1 - Introduction3 lectures • 3min

Introductory Probability Concepts7 lectures • 2hr 48min

Random Variables9 lectures • 3hr

Requirements

Description

Who this course is for: