EXAM P PROBABILITY - Sample Questions

Sep 27, 2026

Exam P Probability sample questions from the Society of Actuaries and the Casualty Actuarial Society cover core probability concepts through multiple choice problems. Topics include inclusion-exclusion for sports viewing, conditional probability with PCP lab/referral outcomes, computations using union and complements for events A and B, and urn sampling with unknown parameters. The set also addresses classification/contingency counting in policyholder demographics, conditional death probabilities given parental heart disease, renewal probabilities with overlapping policy ownership, and patient visit probabilities using differences in marginal probabilities. Additional problems examine car insurance counts and sports-car conditions, independence and joint coverage complements, and joint distribution reasoning for blood pressure and heartbeat categories.

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Exam P Probability

Sample Questions

SOCIETY OF ACTUARIES/CASUALTY ACTUARIAL SOCIETY EXAM P PROBABILITY EXAM P SAMPLE QUESTIONS Copyright 2005 by the Society of Actuaries and the Casualty Actuarial Society Some of the questions in this study note are taken from past SOA/CAS examinations. P-09-05 PRINTED IN U.S.A. 1. A survey of a group’s viewing habits over the last year revealed the following information: (i) 28% watched gymnastics (ii) 29% watched baseball (iii) 19% watched soccer (iv) 14% watched gymnastics and baseball (v) 12% watched baseball and soccer (vi) 10% watched gymnastics and soccer (vii) 8% watched all three sports. Calculate the percentage of the group that watched none of the three sports during the last year. (A) 24 (B) 36 (C) 41 (D) 52 (E) 60 2. The probability that a visit to a primary care physician’s (PCP) office results in neither lab work nor referral to a specialist is 35% . Of those coming to a PCP’s office, 30% are referred to specialists and 40% require lab work. Determine the probability that a visit to a PCP’s office results in both lab work and referral to a specialist. (A) 0.05 (B) 0.12 (C) 0.18 (D) 0.25 (E) 0.35 3. You are given P[A∪B] = 0.7 and P[A∪B′] = 0.9 . Determine P[A] . (A) 0.2 (B) 0.3 (C) 0.4 (D) 0.6 (E) 0.8 4. An urn contains 10 balls: 4 red and 6 blue. A second urn contains 16 red balls and an unknown number of blue balls. A single ball is drawn from each urn. The probability that both balls are the same color is 0.44 . Calculate the number of blue balls in the second urn. (A) 4 (B) 20 (C) 24 (D) 44 (E) 64 5. An auto insurance company has 10,000 policyholders. Each policyholder is classified as (i) young or old; (ii) male or female; and (iii) married or single. Of these policyholders, 3000 are young, 4600 are male, and 7000 are married. The policyholders can also be classified as 1320 young males, 3010 married males, and 1400 young married persons. Finally, 600 of the policyholders are young married males. How many of the company’s policyholders are young, female, and single? (A) 280 (B) 423 (C) 486 (D) 880 (E) 896 6. A public health researcher examines the medical records of a group of 937 men who died in 1999 and discovers that 210 of the men died from causes related to heart disease. Moreover, 312 of the 937 men had at least one parent who suffered from heart disease, and, of these 312 men, 102 died from causes related to heart disease. Determine the probability that a man randomly selected from this group died of causes related to heart disease, given that neither of his parents suffered from heart disease. (A) 0.115 (B) 0.173 (C) 0.224 (D) 0.327 (E) 0.514 7. An insurance company estimates that 40% of policyholders who have only an auto policy will renew next year and 60% of policyholders who have only a homeowners policy will renew next year. The company estimates that 80% of policyholders who have both an auto and a homeowners policy will renew at least one of those policies next year. Company records show that 65% of policyholders have an auto policy, 50% of policyholders have a homeowners policy, and 15% of policyholders have both an auto and a homeowners policy. Using the company’s estimates, calculate the percentage of policyholders that will renew at least one policy next year. (A) 20 (B) 29 (C) 41 (D) 53 (E) 70 8. Among a large group of patients recovering from shoulder injuries, it is found that 22% visit both a physical therapist and a chiropractor, whereas 12% visit neither of these. The probability that a patient visits a chiropractor exceeds by 0.14 the probability that a patient visits a physical therapist. Determine the probability that a randomly chosen member of this group visits a physical therapist. (A) 0.26 (B) 0.38 (C) 0.40 (D) 0.48 (E) 0.62 9. An insurance company examines its pool of auto insurance customers and gathers the following information: (

FAQs

What types of probability topics are included in these Exam P sample questions?

The questions cover inclusion-exclusion, conditional probability, complements and unions of events, urn sampling with unknown counts, and classification-based probability using given totals and overlaps.

How do some questions use conditional information to compute a joint probability?

Several problems provide probabilities of lab work and referrals (or symptoms/conditions) and then ask for the probability of both outcomes occurring together under the specified conditions.

Do the questions include any independence or complement-based reasoning?

Yes. One problem states independence between purchasing collision and disability coverages and uses the joint probability to determine the probability of purchasing neither coverage via complements.

Sep 27, 2026

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