Verified solution · Exam P
This Exam P sample reference tests Mutually Exclusive Events. This problem fills one cell of a two-by-two event partition from its row and column totals. The known intersection forces P(A and D)=0.20, exhausting all of D and leaving P(B and D)=0.00, so choice A.
Independent solution
Setup
Because C and D form a disjoint exhaustive pair, their intersections with A partition event A.
Model
Subtract the supplied A-and-C cell from the A row total to recover the other cell in that row.
Compute
Events A and B also form a disjoint exhaustive pair, so their intersections with D partition event D.
Answer
No probability mass remains in the B-and-D cell.
Continue without hunting through PDFs
The searchable 3108-page manual includes this complete solution, its error analysis, and one original worked variant for every active reference.
Error diagnosis
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
Original practice · fully worked
A routing controller sends files through paths R, S, and T with probabilities 0.25, 0.35, and 0.40. The conditional timeout probabilities on paths R and S are 0.10 and 0.30, respectively. The overall timeout probability is 0.28. Calculate the conditional timeout probability on path T.
Paths R and S contribute timeout probabilities 0.025 and 0.105. The remaining joint weight for path T is 0.28-0.025-0.105=0.150, and dividing by T's routing share 0.40 gives 0.375 and choice D.
Setup
Let Q denote a timeout. Multiply each known route share by its conditional timeout probability.
Model
The three routes are mutually exclusive and exhaustive, so their timeout contributions add to the overall timeout probability.
Compute
Recover path T's joint timeout weight, then divide by the probability of using path T.
Answer
The timeout probability conditional on path T is 0.375.
Keep practicing
These references share syllabus concepts or sit nearby in the official sequence. All 192 Exam P general probability practice problems.
Continue in syllabus order
The 3108-page Probability Proof Manual reorganizes 718 verified Exam P solutions by syllabus skill and adds formula proofs, error patterns, and original worked practice.
ActuaryProof. “SOA Exam P Sample Question #422 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
