Free SOA Exam P (Probability) Practice Questions

The entire SOA Exam P question bank is free: 1,188 practice questions spanning seven core topics in probability essential to actuarial science. From FreeFellow, where 'free' is in the brand name. Public samples need no signup. The full original question bank is free with an account, subject to usage limits.

1,188 questions 7 topics 31 lessons 2026 syllabus
Built by Jeffrey Ting, FSA, CFA, who passed thirteen of the hardest finance exams on the first attempt. The full question bank and worked solutions are free forever.
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Sample Questions

Question 1 Easy
X ~ Beta(3, 2). Find E[X].
Solution
C is correct.

For Beta(α\alpha,β\beta): E[X]E[X] = α\alpha/(α\alpha+β\beta) = 33+2\frac{3}{3+2} = 35\frac{3}{5}.
Question 2 Medium
X ~ Bernoulli(p). Find E[X³].
Solution
E is correct.

Since X only takes values 0 and 1: X^3 = X. Therefore E[X3]E[X^3] = E[X]E[X] = p
Question 3 Hard
X has PDF f(x) = 2/(1+x)³ for x > 0. What is E[X]?
Solution
E is correct.

Verify: ∫0∞2(1+x)3dx=2⋅[−12(1+x)2]0∞=2⋅12=1\int_0^\infty \frac{2}{(1+x)^3}dx = 2 \cdot \left[-\frac{1}{2(1+x)^2}\right]_0^\infty = 2 \cdot \frac{1}{2} = 1. ✓

E[X]=∫0∞2x(1+x)3dxE[X] = \int_0^\infty \frac{2x}{(1+x)^3}dx

Let u=1+xu = 1+x, du=dxdu = dx, x=u−1x = u-1:
=∫1∞2(u−1)u3du=2∫1∞(u−2−u−3)du=2[−u−1+u−22]1∞= \int_1^\infty \frac{2(u-1)}{u^3}du = 2\int_1^\infty (u^{-2} - u^{-3})du = 2\left[-u^{-1} + \frac{u^{-2}}{2}\right]_1^\infty
=2[(0−0)−(−1+1/2)]=2×1/2=1= 2\left[(0-0) - (-1 + 1/2)\right] = 2 \times 1/2 = 1

This is a Pareto II with α=2,θ=1\alpha = 2, \theta = 1: E[X]=θ/(α−1)=1/1=1E[X] = \theta/(\alpha-1) = 1/1 = 1.

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Free practice questions, worked solutions, and written lessons.

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Topics

Deciding between the SOA and CAS tracks? Try the 10-question SOA vs CAS sampler quiz.

Exam P Glossary (37 terms) ›
Exam P Formula Sheet (67 formulas, free PDF) ›

Guides & Articles

Upcoming Exam P Exam Dates (2026)

Dates mark the start of each testing window. Confirm dates directly with the Society of Actuaries before registering.

Exam dateStatus
Nov 4, 2026Confirmed
Jan 14, 2027Confirmed
Mar 1, 2027Confirmed
May 7, 2027Confirmed
Jul 1, 2027Confirmed
Sep 16, 2027Confirmed

Frequently Asked Questions

How many free Exam P practice questions does FreeFellow have?
FreeFellow currently offers 1188 free Exam P practice questions across 7 topics, each with a detailed step-by-step solution. Questions span three difficulty levels and are aligned to the 2026 syllabus. The question bank is updated regularly.
What Exam P topics are covered?
The questions cover 7 topics: Probability Fundamentals, Conditional Probability & Bayes, Discrete Distributions, Continuous Distributions, Joint & Marginal Distributions, and 2 more. Each topic page shows your progress and lets you filter by difficulty level. You can practice by topic to target your weak areas or take mixed-topic practice exams.
How many questions are on the Exam P exam, and how long is it?
The Exam P delivers 30 multiple-choice questions (SOA). Testing time is 3 hours. FreeFellow's Exam P practice questions follow this format, and the free mixed practice draws from the full bank.
Does FreeFellow have Exam P study lessons?
Yes. FreeFellow includes 31 comprehensive text lessons for Exam P, covering key concepts and worked examples for each topic. Lessons are free to read with a free account (no card) and are designed to complement question practice.
Is FreeFellow really free for Exam P prep, or is there a catch?
The full original question bank is free with an account, subject to usage limits. Worked solutions, written lessons, mixed practice, and your readiness score stay free. The original question bank, worked solutions, written lessons, mixed practice, and readiness score stay free forever. Timed mock exams, spaced-repetition flashcards, AI grading on supported exams (5 attempts a day), performance analytics, and a personalized study plan. Practice and grading usage limits apply.
What does the $79 Fellow tier unlock for Exam P?
Fellow is $39 per month or $79 per quarter, per exam family (USD). Fellow Plus is $49 per month, $99 per quarter, or $199 per year, per exam family (USD). Every annual plan is Fellow Plus. Fellow adds timed mock exams with weighted scoring that match the real exam blueprint, spaced-repetition flashcards built on memory science from cognitive psychology, topic-level practice to drill weak areas, performance analytics broken down by topic and difficulty, and a personalized study plan that adapts to your exam date. Everything else (questions, solutions, lessons) stays free.
How does FreeFellow compare to Coaching Actuaries, ASM, or TIA on price?
The full original question bank is free with an account, subject to usage limits. Worked solutions, written lessons, mixed practice, and your readiness score stay free. The original question bank, worked solutions, and written lessons stay free forever. Fellow is $39 per month or $79 per quarter, per exam family (USD). See https://freefellow.org/pricing for package prices and coverage.
How should I use FreeFellow to study for Exam P?
Start with the lessons to build your conceptual foundation, then move to topic-based practice to identify weak areas. As your exam date approaches, switch to timed practice exams under realistic conditions. If you want pacing tools (mock exams, analytics, a study plan) and long-term retention aids (spaced-repetition flashcards), become a Fellow.
What is the Exam P pass rate?
The Exam P pass rate is approximately 45%, based on historical SOA data. Pass rates vary by sitting. The SOA publishes pass rate statistics after each exam window.
How many hours should I study for Exam P?
The SOA recommends 250 to 300 study hours for each preliminary exam. Candidates with strong mathematical backgrounds may need 150 to 200 hours, while those new to the material may need 300 to 350 hours. Consistent daily study over 10 to 14 weeks is more effective than cramming.
What calculator is allowed on Exam P?
The SOA permits a list of Texas Instruments models including the BA II Plus (and Professional), TI-30Xa, TI-30X II, TI-30XS and TI-30XB MultiView, and TI-36X Pro. Most candidates bring the TI-30XS MultiView for statistics-heavy exams and the BA II Plus where time-value-of-money work dominates (FM, FAM, ALTAM).
How is Exam P scored?
SOA preliminary exams are scored on a 0-10 scale, with 6 as the passing threshold. You receive a pass/fail result along with your numeric score. The exam uses multiple-choice questions and the score is based on the number of correct answers.
What is the Exam P exam format?
Exam P is a 3-hour computer-based test with 30 multiple-choice questions, administered at Prometric testing centers. Each question has five answer choices and only one is correct. That works out to 6 minutes per question.

About FreeFellow

Jeffrey Ting, founder of FreeFellow
Jeffrey Ting
FSA, CFA · Founder

FreeFellow was built by Jeffrey Ting, a credentialed actuary and CFA charterholder who has passed thirteen of the hardest exams in finance, all on his first attempt. He paid four-figure prep fees along the way.

So he started writing his own questions, then lessons, then mock exams, until it grew into a full prep platform covering 40 exams with more than 45,000 original practice questions.

01
Cost shouldn't decide who gets in.

A CFA charter, a CPA license, an actuarial credential. Each opens a real career, but prep fees add to the cost of getting there. FreeFellow keeps its original question bank and written lessons free so you can study even if a paid course is out of reach.

02
Free should mean free.

The original question bank, the worked solutions, the topic lessons, mixed practice, and your readiness score stay free, forever. Full access needs a free account, and practice usage limits apply. Fellow adds AI grading on supported exams, spaced-repetition flashcards, full-length mock exams, analytics, and a study plan that adapts to your progress.

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All 1,188 Exam P questions, worked solutions, and lessons are free. The full original question bank is free with an account, subject to usage limits. Worked solutions, written lessons, mixed practice, and your readiness score stay free.

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