Verified solution · Exam P
This Exam P sample reference tests Expected Value. The expected unreduced loss is 30(0.01)+10(0.05)=0.80. A target profit of 0.25 from a premium of 1 leaves 0.75 for expected reimbursement, so the reimbursement share is 0.75/0.80=0.9375, choice E.
Independent solution
Setup
Let F and L count the two covered event types, and let q be the constant share reimbursed.
Model
Linearity of expectation gives the expected gross loss without requiring any dependence assumption between the event counts.
Compute
Set premium less expected reimbursement equal to the target profit and solve for q.
Answer
The company should reimburse 93.75% of each covered loss.
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Original practice · fully worked
An equipment protection cooperative collects an annual fee of 100 dollars per member. A member is expected to incur 0.30 sensor failures costing 80 dollars each and 0.04 power-surge failures costing 400 dollars each during the year. The cooperative reimburses the same fraction of every covered loss and wants expected surplus of 75 dollars per member, with no other expenses. Calculate that reimbursement fraction.
Expected covered loss is 0.30(80)+0.04(400)=40 dollars. The surplus target leaves 25 dollars for reimbursement, so the common fraction is 25/40=0.625, choice D.
Setup
Let q denote the common fraction of each loss paid by the cooperative.
Model
Add frequency times severity across the two failure sources to obtain expected covered loss.
Compute
Equate fee less expected reimbursement to the target surplus.
Answer
The cooperative should reimburse 62.5% of every covered loss.
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ActuaryProof. “SOA Exam P Sample Question #686 — Verified Solution.” Verified 2026-07-30.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-30.
