Verified solution · Exam P
This Exam P sample reference tests Independence. Exactly one event occurs in either the E-only or F-only region. Independence gives probabilities 0.294 and 0.104 for those disjoint regions, totaling 0.398, choice B.
Independent solution
Setup
Split the target into the two mutually exclusive ways that exactly one event can occur.
Model
Use independence for each event-complement pair.
Compute
Evaluate the two disjoint probabilities and add them.
Answer
The exactly-one probability is 0.398.
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Original practice · fully worked
Two detectors operate independently. Detector A signals with probability 0.25, while detector B signals with unknown probability q. Their outputs agree, meaning both signal or neither signals, with probability 0.60. Calculate q.
Agreement has probability 0.25q+0.75(1-q)=0.75-0.50q. Setting this equal to 0.60 gives q=0.30, choice C.
Setup
Represent agreement as the union of two disjoint matching-output cases.
Model
Independence makes each matching-output probability a product.
Compute
Set the agreement expression equal to the observed probability and solve.
Answer
Detector B signals with probability 0.30.
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ActuaryProof. “SOA Exam P Sample Question #210 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
