Verified solution · Exam P
This Exam P sample reference tests Inclusion–Exclusion. Adding the two union probabilities yields the identity 1+P(A), so P(A)=0.7+0.9-1=0.6, choice D.
Independent solution
Setup
Record the probabilities of the two unions that share event A and partition the remaining sample space by B and its complement.
Model
Adding the two union probabilities counts every outcome once and counts outcomes in A one additional time, giving 1+Pr(A).
Compute
Solving 0.7+0.9=1+Pr(A) gives Pr(A)=0.6.
Answer
The required marginal probability is 0.6, so the correct answer is choice D.
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 validation event A is split by whether a separate flag B is present. The recorded probabilities are P(A and B)=0.12 and P(A and not B)=0.28. Find P(A).
The two listed cells are disjoint and exhaust event A, so their sum is 0.40, choice D.
Setup
Partition event A into the disjoint cells where B occurs and where B does not occur.
Model
Because the two cells are disjoint and exhaust A, add their probabilities to recover the marginal probability of A.
Compute
Adding the two recorded cell probabilities gives 0.12+0.28=0.40.
Answer
Thus Pr(A)=0.40, which corresponds to choice D.
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 #3 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
