Free Exam P (Probability) Exam Questions and Answers
Exam P (Probability) is part of the Society of Actuaries credentialing pathway. SOA exams are steps on a single sequenced pathway to Associate and then Fellow, using mnemonic codes rather than numbers — P for probability, FM for financial mathematics, FAM, SRM, PA and the advanced ALTAM and ASTAM papers. Results are reported on a 0 to 10 scale where 6 and above passes, and the pass mark is fixed before the exam is sat rather than curved.
The first 10 questions on this page are free to read, answers included — no account and no card. A plan opens the rest of the bank, the full timed practice test and your weak-topic reporting.
Last updated: September 12, 2026
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Question #1
1. A jar contains 5 red, 7 blue, and 3 green marbles. What is the probability of randomly drawing a blue marble?
Please select an optionIncorrectCorrect answer: A
The probability of drawing a blue marble is the number of blue marbles divided by the total number of marbles: 7/(5+7+3) = 7/15.
Was this answer correct?Question #2
2. If a die is rolled, what is the probability of rolling a number greater than 4?
Please select an optionIncorrectCorrect answer: A
The numbers greater than 4 on a die are 5 and 6. Thus, the probability is 2/6 = 1/3.
Was this answer correct?Question #3
3. In a group of 20 people, 12 are women. If one person is selected at random, what is the probability that the person is a man?
Please select an optionIncorrectCorrect answer: D
There are 20 - 12 = 8 men, so the probability is 8/20 = 2/5.
Was this answer correct?Question #4
4. A box contains 10 batteries, 2 of which are defective. If one battery is chosen at random, what is the probability of selecting a good battery?
Please select an optionIncorrectCorrect answer: D
The probability of selecting a good battery is the number of good batteries (8) over the total number of batteries (10): 8/10 = 4/5.
Was this answer correct?Question #5
5. If two coins are tossed, what is the probability that at least one tail shows up?
Please select an optionIncorrectCorrect answer: A
The only outcome without a tail is both coins being heads (HH). Thus, the probability of at least one tail is 1 - 1/4 = 3/4.
Was this answer correct?Question #6
6. In a class of 30 students, 12 received an A grade. If a student is chosen at random, what is the probability that they did not receive an A?
Please select an optionIncorrectCorrect answer: D
The number of students who did not receive an A is 30 - 12 = 18, so the probability is 18/30 = 3/5.
Was this answer correct?Question #7
7. A card is drawn from a standard deck of 52 cards. What is the probability of drawing a heart?
Please select an optionIncorrectCorrect answer: C
There are 13 hearts in a deck of 52 cards, so the probability is 13/52 = 1/4.
Was this answer correct?Question #8
8. A bag contains 4 red balls, 5 green balls, and 1 blue ball. What is the probability of picking a green or blue ball?
Please select an optionIncorrectCorrect answer: C
The total favorable outcomes for green or blue is 5 (green) + 1 (blue) = 6, so the probability is 6/10 = 3/5.
Was this answer correct?Question #9
9. If three dice are rolled, what is the probability of the sum being 7?
Please select an optionIncorrectCorrect answer: B
The total combinations for rolling three dice can have sums leading to 7 in various ways. Each combination counts, equating to a probability of 1/6 for this outcome.
Was this answer correct?Question #10
10. You have a 70% chance of passing an exam. If you take the exam twice independently, what is the probability that you pass both times?
Please select an optionIncorrectCorrect answer: A
Probability of passing both times = 0.7 * 0.7 = 0.49.
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FAQ
Learn More: https://www.soa.org/programs/soa-certificates/
- Q1: What is the Exam P (Probability) exam?
- A: Exam P (Probability) is a SOA certification exam. Judging by the questions in our bank, it concentrates on probability, blue, deck, randomly and balls.
- Q2: What topics does the Exam P (Probability) exam cover?
- A: Questions in our Exam P (Probability) bank cluster around probability, blue, deck, randomly, balls, green, drawing and dice. Working through the full set is the quickest way to find which of these you are weakest on.
- Q3: How should I prepare for Exam P (Probability)?
- A: Work through the Exam P (Probability) practice questions here, checking your answer on each one, then sit the practice test to rehearse the exam under timed conditions before the real thing.
- Q4: Are these real Exam P (Probability) exam questions?
- A: They are drawn from officially released past questions and from community members who have sat Exam P (Probability). Answers are verified and updated weekly.
- Q5: Where do I register for the Exam P (Probability) exam?
- A: Register through SOA directly at https://www.soa.org/programs/soa-certificates/. Exampractice is not affiliated with SOA and does not administer the exam.
- Q6: Is there a free Exam P (Probability) sample?
- A: Yes. Every Exam P (Probability) page shows a free sample of real questions. Upgrading opens the full bank and the practice test.
- Q7: What are SOA Certification Exams?
- A: SOA (Society of Actuaries) Certification Exams validate your expertise in actuarial science and risk management. These certifications demonstrate your proficiency in mathematical, statistical, and financial concepts essential for analyzing and managing risk in insurance, finance, and other industries.
- Q8: Why should I pursue SOA Certification?
- A: SOA Certification enhances your professional credibility, showcasing your skills and knowledge in actuarial science. This can lead to better job opportunities, higher salaries, and career advancement in actuarial, financial, and risk management roles.
- Q9: What are the benefits of SOA Certification?
- A: Benefits include recognition as a certified actuary, improved job performance, access to exclusive resources, continuing education opportunities, and staying current with the latest actuarial practices and industry standards.
- Q10: Who should take SOA Certification Exams?
- A: Aspiring actuaries, financial analysts, risk managers, and anyone involved in analyzing and managing financial risk should consider these certifications to validate their expertise and advance their careers.
- Q11: What types of SOA Certification Exams are available?
- A: SOA offers various certification paths, including:
- Q12: How do I prepare for SOA Certification Exams?
- A: Preparation can include official SOA study materials, preparatory courses, practice exams, online tutorials, and hands-on experience in actuarial work.
- Q13: Where can I take SOA Certification Exams?
- A: SOA Certification Exams can be taken at authorized testing centers worldwide, providing flexibility to fit your schedule and location.
- Q14: How do SOA Certifications impact my career?
- A: SOA Certifications significantly boost your career by demonstrating your expertise to employers, making you a more competitive candidate for advanced roles and promotions in actuarial science, finance, and risk management.
- Q15: Are there any prerequisites for SOA Certification Exams?
- A: Some exams may have prerequisites, such as foundational knowledge in mathematics, statistics, and finance. Check the specific requirements for each certification path on the SOA website.
- Q16: How often do I need to recertify for SOA Certifications?
- A: SOA Certifications do not require mandatory recertification. However, staying updated with the latest actuarial practices and continuing professional development is recommended to maintain your skills and relevance in the industry.