Verified solution · Exam P
This Exam P sample reference tests Set Probability. Complementing the two supplied percentages gives probabilities 0.60 for the three-year event and 0.30 for combined coverage. The availability restrictions make these events disjoint, so their union has probability 0.90 and choice E.
Independent solution
Setup
Let T be the event of a three-year contract and B the event of combined parts-and-labor coverage.
Model
The availability table permits no three-year contract with combined coverage, so the two events have empty intersection.
Compute
Apply the addition rule for the union and use the structural zero for the intersection.
Answer
Nine tenths of the contracts satisfy at least one of the two conditions.
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Original practice · fully worked
Every observation block at a research observatory uses an optical instrument, a radio instrument, or both. Sixty-five percent of blocks use exactly one instrument. Also, 52 percent occur during daylight or twilight. A safety rule prohibits blocks using both instruments from being scheduled at night. Calculate the probability that a randomly selected block is at night or uses both instruments.
Night blocks have probability 0.48 and dual-instrument blocks have probability 0.35. The safety rule makes those events disjoint, so their union is 0.83 and choice E.
Setup
Let N denote a night block and D a block using both instruments. Convert the supplied complementary percentages.
Model
The scheduling rule excludes every dual-instrument block from the night period.
Compute
Add the probabilities of the two disjoint events.
Answer
The requested union contains 83 percent of the scheduled blocks.
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ActuaryProof. “SOA Exam P Sample Question #691 — Verified Solution.” Verified 2026-07-30.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-30.
