200+ Free SOA Exam P Practice Questions

Pass your SOA Exam P Probability exam on the first try — instant access, no signup required.

✓ No registration✓ No credit card✓ No hidden fees✓ Start practicing immediately

200+ Questions

100% Free

1 / 200

Question 1

Score: 0/0

In a group of 120 candidates, 68 passed a probability quiz, 54 passed a statistics quiz, and 26 passed both quizzes. How many candidates passed neither quiz?

to track

2026 Statistics

Key Facts: SOA Exam P Exam

Official Questions

SOA syllabus

3 hrs

Time Limit

SOA syllabus

6-10

Passing Grades

SOA grading scale

$275

Standard Fee

SOA fee table

Weighted Domains

SOA syllabus

Jan 13, 2026

Latest Update

SOA updates page

As of March 11, 2026, SOA lists Exam P at $275 with a 30-question, 3-hour computer-based format delivered through Prometric. The current SOA syllabus weights Univariate Random Variables most heavily at 44-50%, while General Probability and Multivariate Random Variables each account for 23-30%. SOA reports results on a 0-10 scale with 6-10 passing, does not publish a fixed raw cut score, and on January 13, 2026 updated the official sample questions and sample solutions for Exam P.

Sample SOA Exam P Practice Questions

Try these sample questions to test your SOA Exam P exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 200+ question experience with AI tutoring.

1In a group of 120 candidates, 68 passed a probability quiz, 54 passed a statistics quiz, and 26 passed both quizzes. How many candidates passed neither quiz?

A.24

B.96

C.94

D.52

Explanation: Use inclusion-exclusion first: |A union B| = 68 + 54 - 26 = 96. The number who passed neither quiz is the complement, so 120 - 96 = 24. On Exam P, inclusion-exclusion and complements are often tested together.

2In a group of 150 candidates, 83 passed a probability quiz, 71 passed a statistics quiz, and 29 passed both quizzes. How many candidates passed neither quiz?

A.125

B.25

C.121

D.67

Explanation: Use inclusion-exclusion first: |A union B| = 83 + 71 - 29 = 125. The number who passed neither quiz is the complement, so 150 - 125 = 25. On Exam P, inclusion-exclusion and complements are often tested together.

3At a recruiting event, 112 students are interested in life contingencies, 95 are interested in risk modeling, and 44 are interested in both. How many students are interested in at least one of the two topics?

A.207

B.37

C.163

D.119

Explanation: The required count is |A union B| = |A| + |B| - |A intersection B|. Substituting gives 112 + 95 - 44 = 163. If you forget to subtract the overlap, everyone interested in both topics gets counted twice.

4In a group of 180 candidates, 97 passed a probability quiz, 88 passed a statistics quiz, and 35 passed both quizzes. How many candidates passed neither quiz?

A.150

B.145

C.83

D.30

Explanation: Use inclusion-exclusion first: |A union B| = 97 + 88 - 35 = 150. The number who passed neither quiz is the complement, so 180 - 150 = 30. On Exam P, inclusion-exclusion and complements are often tested together.

5At a recruiting event, 84 students are interested in life contingencies, 73 are interested in risk modeling, and 31 are interested in both. How many students are interested in at least one of the two topics?

A.126

B.157

C.34

D.95

Explanation: The required count is |A union B| = |A| + |B| - |A intersection B|. Substituting gives 84 + 73 - 31 = 126. If you forget to subtract the overlap, everyone interested in both topics gets counted twice.

6In a group of 140 candidates, 79 passed a probability quiz, 64 passed a statistics quiz, and 28 passed both quizzes. How many candidates passed neither quiz?

A.115

B.25

C.112

D.61

Explanation: Use inclusion-exclusion first: |A union B| = 79 + 64 - 28 = 115. The number who passed neither quiz is the complement, so 140 - 115 = 25. On Exam P, inclusion-exclusion and complements are often tested together.

7A probability model assigns probability 7/12 to selecting a policyholder with at least one prior claim. What is the probability of the complement of that event?

A.7/12

B.5/7

C.5/12

D.1/2

Explanation: Complementary events add to 1. So the required probability is 1 - 7/12 = 5/12. Using complements is often faster than counting the opposite event directly.

8A probability model assigns probability 11/20 to drawing a ticket that requires manual review. What is the probability of the complement of that event?

A.11/20

B.9/11

C.1/2

D.9/20

Explanation: Complementary events add to 1. So the required probability is 1 - 11/20 = 9/20. Using complements is often faster than counting the opposite event directly.

9A probability model assigns probability 13/18 to an underwriting file being complete on first submission. What is the probability of the complement of that event?

A.5/18

B.13/18

C.5/13

D.1/3

Explanation: Complementary events add to 1. So the required probability is 1 - 13/18 = 5/18. Using complements is often faster than counting the opposite event directly.

10A probability model assigns probability 5/8 to a randomly chosen applicant accepting the quoted premium. What is the probability of the complement of that event?

A.5/8

B.3/8

C.3/5

D.1/2

Explanation: Complementary events add to 1. So the required probability is 1 - 5/8 = 3/8. Using complements is often faster than counting the opposite event directly.

About the SOA Exam P Exam

The SOA Exam P Probability exam is a core preliminary actuarial exam that tests probability foundations, univariate distributions, insurance-payment adjustments, and multivariate random-variable techniques used in actuarial work.

Assessment

30 multiple-choice questions

Time Limit

3 hours

Passing Score

Grade of 6 or higher on SOA's 0-10 scale

Exam Fee

$275 (Society of Actuaries (SOA) / Prometric)

SOA Exam P Exam Content Outline

23-30%

General Probability

Master set notation, axioms of probability, addition and multiplication rules, conditional probability, independence, counting methods, Bayes theorem, and the law of total probability.

44-50%

Univariate Random Variables

Work with discrete and continuous distributions, cumulative distribution functions, moments, percentiles, variance, and insurance-payment adjustments such as deductibles, coinsurance, limits, and inflation.

23-30%

Multivariate Random Variables

Handle joint, marginal, and conditional discrete distributions, covariance and correlation, order statistics, linear combinations of random variables, and Central Limit Theorem applications.

How to Pass the SOA Exam P Exam

What You Need to Know

Passing score: Grade of 6 or higher on SOA's 0-10 scale
Assessment: 30 multiple-choice questions
Time limit: 3 hours
Exam fee: $275

Keys to Passing

Complete 500+ practice questions
Score 80%+ consistently before scheduling
Focus on highest-weighted sections
Use our AI tutor for tough concepts

SOA Exam P Study Tips from Top Performers

1Memorize the core probability identities well enough that complements, conditional probability, and Bayes updates become setup work instead of derivations under time pressure.

2Do not treat univariate distributions as isolated formulas. Practice recognizing when a problem is really about selecting the right model, then extracting moments, percentiles, or payment adjustments from it.

3Spend time on insurance-payment transformations because deductibles, coinsurance, policy limits, and inflation translate pure probability knowledge into actuarial-style applications.

4For multivariate questions, force yourself to label whether you need a joint, marginal, or conditional quantity before you compute anything. That prevents many avoidable algebra mistakes.

5Run timed sets with a calculator and normal table workflow that matches test conditions so your exam pace reflects the actual 3-hour constraint.

Frequently Asked Questions

How many questions are on SOA Exam P?

The current SOA Probability syllabus lists 30 multiple-choice questions. SOA also notes that a few pilot items may appear in the computer-based pool, but only scored questions count toward the result.

How long is the SOA Exam P exam?

You get 3 hours to complete Exam P. Because many items are calculation-heavy, you need both probability fluency and disciplined time management.

What is the passing score for SOA Exam P?

SOA reports preliminary exam grades on a 0-10 scale, and grades from 6 to 10 are passing. SOA does not publish one fixed raw percentage because the final pass mark is set for each sitting.

Which topics matter most on Exam P?

Univariate Random Variables is the largest domain at 44-50% of the syllabus. General Probability and Multivariate Random Variables are each 23-30%, so they still represent substantial portions of the exam.

What changed for SOA Exam P in 2026?

The official Exam P updates page shows a January 13, 2026 refresh to the sample questions and sample solutions. As of March 11, 2026, SOA still lists the current standard fee at $275 and continues offering Exam P in multiple CBT windows under its ongoing registration model for P and FM.

Do I need Exam P for the ASA pathway?

Yes. SOA's ASA requirements page still lists Probability (P) as one of the foundational exam requirements on the associate-level pathway. It is commonly one of the first actuarial exams candidates attempt.