Verified solution · Exam P
This Exam P sample reference tests Set Operations. Removing the triple region gives 82 in life-mutual only and 77 in annuity-mutual only, leaving 45 in mutual only. The exactly-one total then yields 100 in annuity only and 145 in life only; the remaining annuity-life region has 35. All seven regions total 500, choice D.
Independent solution
Setup
Convert the two inclusive mutual-fund intersections to pair-only counts and recover the mutual-only region.
Model
Let x be the annuity-only count; the life-only count is x plus 45. Use the total owning exactly one type.
Compute
Use the annuity marginal to obtain the last pair-only region and sum the partition.
Answer
The agent has 500 clients owning at least one listed product.
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Original practice · fully worked
A platform has 400 accounts. Fifty-five percent enable backups. Among backup-enabled accounts, 30% also enable encryption; among accounts without backups, 20% enable encryption. Calculate the number of accounts that enable exactly one of the two features.
There are 220 backup-enabled accounts, of which 154 lack encryption. Of the 180 accounts without backups, 36 enable encryption. These two exactly-one regions total 190, choice D.
Setup
Split the account population by backup status.
Model
Calculate the two disjoint regions in which exactly one feature is enabled.
Compute
Add the backup-only and encryption-only regions.
Answer
Exactly 190 accounts enable one feature.
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ActuaryProof. “SOA Exam P Sample Question #183 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
