Verified solution · Exam P
This Exam P sample reference tests Conditional Probability. The conditional-probability ratio implies that the fire marginal is twice the flood marginal. The outside-versus-overlap relation then makes their marginal sum 0.80, so the flood probability is 0.80/3=0.2667 and choice A.
Independent solution
Setup
Let f and w be the two policy marginals and let j be their positive intersection probability.
Model
Translate the ratio of the two reverse conditional probabilities. Positivity of j permits cancellation.
Compute
Express the outside cell using inclusion-exclusion and apply its stated difference from the intersection.
Answer
The flood-policy marginal rounds to 0.27.
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Original practice · fully worked
On a fleet-monitoring day, event H means at least one heat alert and event V means at least one vibration alert. Suppose P(H)=0.40, P(H union V)=0.65, and P(V given H)=0.25. Calculate P(H given V).
The forward conditional probability gives an intersection of 0.10. Inclusion-exclusion then gives P(V)=0.35, so the reverse conditional probability is 0.10/0.35=2/7 and choice C.
Setup
Convert the supplied forward conditional probability into the joint alert probability.
Model
Use inclusion-exclusion to recover the vibration-alert marginal from the union, the heat marginal, and the intersection.
Compute
Solve for P(V), then condition the joint alert probability on V.
Answer
The reverse conditional probability rounds to 0.286.
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ActuaryProof. “SOA Exam P Sample Question #528 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
