Verified solution · Exam P
This Exam P sample reference tests Bayes' Theorem. This is an inverse Bayes calculation for an unknown within-group rate. If x is the female smoking rate, then the female and male smoker contributions are 0.4x and 0.12; requiring women to be 20% of all smokers gives x=0.075, or 7.50%, and choice A.
Independent solution
Setup
Let x denote the unknown smoking probability within the female group and form the two smoker contributions.
Model
Express the supplied female share among smokers as a Bayes ratio.
Compute
Solve the resulting linear equation for the within-group rate.
Answer
The smoking rate among female policyholders is 7.50%.
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Error diagnosis
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Original practice · fully worked
A workflow processes 40% of jobs in standard mode, 35% in advanced mode, and 25% in diagnostic mode. A standard job produces one audit record, an advanced job produces two, and a diagnostic job produces four. One audit record is selected uniformly from all records. Calculate the probability that its job used diagnostic mode.
Record sampling weights each job mode by its number of records. The standard, advanced, and diagnostic contributions are 0.40, 0.70, and 1.00 records per job, so diagnostic mode supplies 1/2.1=10/21≈0.476 of all records and choice C.
Setup
Weight each job-mode frequency by the number of records that one job in that mode creates.
Model
A uniformly sampled record comes from a mode in proportion to that mode's record contribution.
Compute
Normalize the diagnostic contribution by the total number of records generated per job.
Answer
The sampled record has diagnostic-mode origin with probability approximately 0.476.
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These references share syllabus concepts or sit nearby in the official sequence. All 192 Exam P general probability practice problems.
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ActuaryProof. “SOA Exam P Sample Question #334 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
