Verified solution · Exam P
This Exam P sample reference tests Set Counting. This is a three-set membership-count problem. Membership totals show that 450 drivers have exactly two factors; adding 1,200 with exactly one, 300 with all three, and 500 with none gives 2,450 and choice C.
Independent solution
Setup
Group drivers by how many of the three factors they exhibit. The three exactly-one regions contain 1,200 drivers in total.
Model
Summing the three individual factor counts counts an exactly-two driver twice and an all-three driver three times.
Compute
Solve for the number with exactly two factors, then add the disjoint membership classes and the no-factor class.
Answer
The study contains 2,450 drivers.
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Original practice · fully worked
A laboratory audits 600 samples using flags A, B, and C. The individual flag counts are 280, 250, and 220. The inclusive pairwise intersection counts are 120, 90, and 80, and 40 samples carry all three flags. Among samples bearing one or more flags, determine the proportion bearing exactly one.
Inclusion-exclusion gives 500 samples with at least one flag. Removing repeated pair and triple memberships gives 290 samples with exactly one flag, so the conditional probability is 290/500=0.58 and choice E.
Setup
Apply three-set inclusion-exclusion to count samples carrying at least one flag.
Model
Recover the exactly-one count from the individual, inclusive pairwise, and triple counts.
Compute
Evaluate the exactly-one count and normalize it within the flagged samples.
Answer
Among flagged samples, 58.0 percent carry exactly one flag.
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ActuaryProof. “SOA Exam P Sample Question #258 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
