Verified solution · Exam P
This Exam P sample reference tests Inclusion-Exclusion. Three-set inclusion-exclusion gives 450 policies having at least one listed home feature. Subtracting this union from the 1000-policy portfolio leaves 550 with none, choice D.
Independent solution
Setup
Let A, B, and C denote the three listed home-feature sets.
Model
Apply three-set inclusion-exclusion using inclusive pair intersections.
Compute
Evaluate the union and take its complement in the portfolio.
Answer
There are 550 policies with none of the three features.
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Original practice · fully worked
Three independent sensors trigger during a test with probabilities 0.25, 0.40, and 0.10. Calculate the probability that exactly one sensor triggers.
The three disjoint one-trigger cases have probabilities 0.135, 0.270, and 0.045. Their sum is 0.450, choice D.
Setup
List the three mutually exclusive ways exactly one sensor can trigger.
Model
Use independence to multiply each trigger probability by the other two non-trigger probabilities.
Compute
Evaluate and add the disjoint cases.
Answer
The probability of exactly one trigger is 0.45.
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ActuaryProof. “SOA Exam P Sample Question #184 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
