[[Actuarial Notes Wiki|Wiki]] / **Exam P-1 (SOA)** <div class="exam-nav" data-color="#2563eb" data-current="P-1|Probability" data-tracks="ASA|Associate of the Society of Actuaries (ASA).md,ACAS|Associate of the Casualty Actuarial Society (ACAS).md" </div> ## Exam P-1 (SOA) The **Probability (P-1) Exam** is a 3 hour exam with 30 multiple choice questions about probability theory concepts and their application to measuring risk. <div class="callout-cols-2"> > [!answer]- 📅 Exam Schedule {2026} > > <div class="highlight-upcoming" data-date-col="0"></div> > > Dates | Exams > -|- > Mar 9 - Mar 20 | P >May 8 - May 19 | P >Jul 8 - Jul 19 | P >Sep 10 - Sep 21 | P >Nov 4 - Nov 15 | P > >- [Register](https://www.soa.org/education/exam-req/registration/edu-registration/) ($275 USD registration fee) > [!answer]- 📄 Download Resources {4 PDFs} > - [Exam P-1 Syllabus](https://www.soa.org/globalassets/assets/files/edu/2026/spring/syllabi/2026-03-exam-p-syllabus.pdf) > - [May 2026 Exam P-1 Syllabus](https://www.soa.org/globalassets/assets/files/edu/2026/spring/syllabi/2026-05-exam-p-syllabus.pdf) > - [736 Sample Questions for Exam P (SOA)](https://www.soa.org/globalassets/assets/files/edu/2026/spring/questions-solutions/2026-05-exam-p-sample-questions.pdf) > - [Sample Answers](https://www.soa.org/globalassets/assets/files/edu/2025/fall/questions-solutions/2025-10-exam-p-sample-solutions.pdf) </div> >[!answer]- 📕 Source Material {6 Textbooks} > > | Source | Coverage | | ----------------------------------------------------------------------------------------- | --------------------------------------------------------------------------------------------------- | | [[A First Course in Probability (Ross - 2019)]] | Chapters 1-8^[Excluding 4.8.4, 5.6.2, 5.6.3, 5.6.5, 5.7, 7.2.1, 7.2.2, 7.3, 7.6, 7.7, 7.8, 7.9]<br> | | [[Mathematical Statistics with Applications (Wackerly, Mendenhall, & Scheaffer - 2008)]] | Chapters 1-8^[Exlcuding 2.12, MGF, 4.10, Continuous Multivariate Distributions, 5.10, 7.4] | | [[Probability for Risk Management (Hassett - 2021)]] | Chapters 1-11 | | [[Probability and Statistics with Applications - A Problem Solving Text (Asimow - 2021)]] | Chapters 1-8 | | [[Probability and Statistical Inference (Hogg - 2020)]] | Chapters 1-5 | | [[Probability (Leemis - 2018)]] | Chapters 1-8 | ### Prerequisite knowledge Knowledge of the following concepts is expected: - [[Calculus]], including series, differentiation, and integration. - Concepts introduced in [Risk and Insurance](https://www.soa.org/49355c/globalassets/assets/files/edu/p-21-05.pdf) ### Learning Objectives > [!example]- General Probability {23-30%} > ### General Probability > Understand basic concepts of [[Probability]] and [[Discrete Mathematics]]. > 1. Define [[Set Function]], [[Venn Diagram]], [[Sample Space]], and [[Event]]. Define **probability** as a set function on a collection of events and state the basic [[Axioms of Probability]]. > 2. Calculate **probabilities** using [[Combinatorics]], such as [[Combination]] and [[Permutation]]. > 3. Define [[Independent Events|Independence]] and calculate probabilities of [[Independent Events]]. > 4. Calculate probabilities of [[Mutually Exclusive Events]]. > 5. Calculate probabilities using [[Probability Addition Rule]] and [[Probability Multiplication Rule|Probability Multiplication Rules]]. > 6. Define and calculate [[Conditional Probability]]. > 7. State [[Bayes Theorem]] and [[The Law of Total Probability]] and use them to calculate conditional probabilities. > > [!example]- Univariate Random Variables {44-50%} > ### Univariate Random Variables > Understand [[Discrete Univariate Distributions]] and [[Continuous Univariate Distributions]] and their applications. >1. Explain and apply the concepts of [[Probability]], [[Random Variable|Random Variables]], probability density functions, and cumulative distribution functions. > 2. Calculate [[Conditional Probability|Conditional Probabilities]]. > 3. Explain and calculate expected values, including moments, mode, median, and percentiles. > 4. Explain and calculate [[Variance]], [[Standard Deviation]], and [[Coefficient of Variation]]. > 5. Calculate the amount that an insurance company pays to a policyholder for a claim given [[Policy Information]], including [[Deductibles]], [[Coinsurance Percentages]], and [[Benefit Limits]], as well as other factors, such as [[Inflation]]. > 6. Calculate the [[Expected Value]], [[Variance]], and [[Standard Deviation]] of both the [[Loss Random Variable]] and the corresponding [[Payment Random Variable]]. > > #### Discrete Univariate Distributions > - [[Binomial]] > - [[Geometric]] > - [[Hypergeometric]] > - [[Negative Binomial]] > - [[Poisson]] > - [[Uniform]] > > #### Continuous Univariate Distributions > - [[Beta]] > - [[Exponential]] > - [[Gamma]] > - [[Lognormal]] > - [[Normal]] > - [[Uniform]] > [!example]- Multivariate Random Variables {23-30%} > ### Multivariate Random Variables > Understand key concepts in the discrete and continuous settings concerning [[Multivariate Distribution]]s, the [[Distribution of Order Statistics]] for [[Independent Random Variables]], and linear combinations of independent random variables, along with associated applications. > 1. Determine [[Joint Probability Functions]] and [[Joint Cumulative Distribution Functions]] for discrete random variables. > 2. Determine [[Conditional Probability Function]] and [[Marginal Probability Function]] for discrete random variables. > 3. Calculate [[Moments for Joint Distributions]] for joint, conditional, and marginal discrete distributions. > 4. Calculate [[Variance for Conditional Distributions|Variance]] and standard deviation for conditional and marginal probability distributions for discrete random variables. > 5. Calculate the [[Covariance]] and the [[Correlation Coefficient]] for discrete random variables. > 6. Determine the [[Joint Distribution of Order Statistics]] for a set of independent random variables. > 7. Calculate [[Probabilities for Linear Combinations]] of independent discrete random variables as well as for continuous normal random variables. > 8. Calculate [[Moments for Linear Combinations]] of independent random variables. > 9. Apply the [[Central Limit Theorem]] to calculate approximations of probabilities for linear combinations of independent and identically distributed random variables.