SOA Exam P Guide
Exam P is the SOA probability exam: a 3-hour, 30-question, multiple-choice CBT exam covering general probability, univariate random variables, and multivariate random variables.
What Exam P Entails
- Probability theory, random variables, and distributions applied to actuarial risk.
- Calculus fluency, especially integration, differentiation, and series where probability calculations require them.
- Core practice: conditioning correctly, identifying distributions, computing expectations, and handling multivariate probability.
SOA Exam P
Official syllabus facts are mapped; sample questions are available for topic tagging only.
What the official PDFs establish
- Purpose
- Fundamental probability tools for quantitatively assessing risk, with actuarial applications emphasized.
- Scoring note
- Unanswered questions are scored incorrect; candidates should answer every question.
Topic and domain coverage
| Topic | Weight | Source |
|---|---|---|
| General Probability | 23-30% | Source: Exam P syllabus, p. 2 |
| Univariate Random Variables | 44-50% | Source: Exam P syllabus, p. 3 |
| Multivariate Random Variables | 23-30% | Source: Exam P syllabus, p. 4 |
Chapter and reading intelligence
- Risk and insurance background
Use the SOA risk and insurance note for insurance-context vocabulary and examples, not as a substitute for probability practice.
Source: Risk and Insurance
Official files used by the map
- Official syllabussyllabus
Primary source for format, assumptions, topic weights, and learning outcomes.
Source: Exam P - July 2026 Syllabus - Sample questionssample-questions
Use internally for coverage tagging and practice-pattern planning; do not republish questions.
Source: Exam P Sample Questions
Quick Facts
The July 2026 SOA syllabus describes Exam P as a three-hour, 30-question, multiple-choice, computer-based exam. The largest topic block is univariate random variables, weighted at 44-50%.
- General probability: 23-30%.
- Univariate random variables: 44-50%.
- Multivariate random variables: 23-30%.
What To Study First
Start with problem types, not formula memorization. The highest-return loop is conditional probability, expected value, distribution recognition, insurance payment transformations, joint distributions, and normal approximation.
Statistics And ML Connection
Exam P is also the probability foundation behind classification, count models, expected loss, simulation, calibration, survival models, and uncertainty quantification.
Original exam practice
3 questions built from syllabus outcomes and released-exam patterns. The prompts and answers are original, so they train the skill without copying official exam text.
Exam P Core Probability Drill
Original Exam P checks for conditioning, expected value, variance, and distribution choice.
- Question 1/Calculation
Conditional probability with a flag
Two percent of policies are high risk. A screening flag catches 80 percent of high-risk policies and falsely flags 10 percent of other policies. Among flagged policies, what percent are high risk?
Solution and grading points
High-risk flagged policies contribute 0.80 x 0.02 = 0.016. All flagged policies contribute 0.016 + 0.10 x 0.98 = 0.114. The answer is 0.016 / 0.114 = 0.140, or 14.0 percent.
- Uses Bayes' theorem with the flag as the conditioning event.
- Includes false positives from non-high-risk policies.
- Interprets the answer as about 14 percent, not 80 percent.
- Question 2/Calculation
Mixture expected value
A claim amount is exponential with mean 500 for 70 percent of policies and exponential with mean 2,000 for 30 percent. What is the portfolio mean claim amount?
Solution and grading points
The mixture mean is 0.70(500) + 0.30(2,000) = 950.
- Uses the law of total expectation.
- Weights means by class probabilities.
- Does not average the exponential rates instead of the means.
- Question 3/Calculation
Variance decomposition
Let E[X | Y] = 10 + 2Y and Var(X | Y) = 9. If Var(Y) = 4, find Var(X).
Solution and grading points
Var(X) = E[Var(X | Y)] + Var(E[X | Y]) = 9 + Var(10 + 2Y) = 9 + 4Var(Y) = 25.
- Uses total variance.
- Keeps the conditional variance term.
- Squares the coefficient 2 when computing Var(10 + 2Y).