Verified solution · Exam P
This Exam P sample reference tests Conditional Distributions. First average the conditional low-cost probabilities over the market states to obtain 0.32. The complementary high-cost probability is 0.68, so the expected cost is 5(0.32)+10(0.68)=8.4 million, choice D.
Independent solution
Setup
Use the market-state probabilities to remove the conditioning from the two-point cost distribution.
Model
Weight each conditional low-cost probability by its corresponding market-state probability.
Compute
Complete the marginal cost distribution and take its expectation, in millions.
Answer
The expected recall cost is 8.4 million.
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Original practice · fully worked
A field station faces either a 2-thousand-dollar routine repair or an 8-thousand-dollar major repair. Weather is clear, rainy, or snowy with probabilities 0.50, 0.30, and 0.20. Conditional on those states, the probabilities of a major repair are 0.10, 0.40, and 0.80, respectively. Calculate the expected repair cost.
The total probability of a major repair is 0.50(0.10)+0.30(0.40)+0.20(0.80)=0.33. The expected cost is therefore 2(0.67)+8(0.33)=3.98 thousand dollars, choice C.
Setup
Average the major-repair probabilities over the weather distribution.
Model
Insert the three weather-state probabilities.
Compute
Use the resulting two-point distribution for repair cost, measured in thousands.
Answer
The expected repair cost is 3.98 thousand dollars.
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ActuaryProof. “SOA Exam P Sample Question #716 — Verified Solution.” Verified 2026-07-30.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-30.
