Verified solution · Exam P
This Exam P sample reference tests Bayes' Theorem. Female contributors supply probability mass 0.45(0.20)=0.09, while male contributors supply 0.55(0.30)=0.165. Bayes' theorem gives 0.09/(0.09+0.165)=6/17=0.352941, so choice C.
Independent solution
Setup
Let F identify a female employee and C identify plan contribution.
Model
Weight each category-specific contribution rate by its employee share.
Compute
Normalize the female-contributor mass over all contributors.
Answer
The conditional probability rounds to 0.35.
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Original practice · fully worked
A routing device selects tray A with probability 0.40 and tray B otherwise. Tray A contains four copper pieces and two glass pieces; tray B contains one copper piece and five glass pieces. Two pieces are drawn without replacement from the selected tray, and their materials are different. Calculate the conditional probability that tray A was selected.
The unlike-material likelihoods are 8/15 for tray A and 1/3 for tray B. Prior weighting gives contributions 16/75 and 15/75, so the posterior tray-A probability is 16/31=0.5161 and choice C.
Setup
Let D denote the observation that the two materials differ. Compute its likelihood under each tray.
Model
Weight the two unlike-material likelihoods by the tray-selection probabilities.
Compute
Normalize the tray-A contribution over both possible sources of unlike materials.
Answer
The posterior tray-A probability rounds to 0.5161.
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These references share syllabus concepts or sit nearby in the official sequence. All 192 Exam P general probability practice problems.
Drill the method: Exam P Conditional Probability problems
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ActuaryProof. “SOA Exam P Sample Question #264 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
