Verified solution · Exam P
This Exam P sample reference tests Bayes' Theorem. The zero-count likelihoods are exp(-0.5) and exp(-1) for the two intersection classes. Bayes' theorem gives 0.4exp(-0.5)/[0.4exp(-0.5)+0.6exp(-1)]=0.5236, so choice D is correct.
Independent solution
Setup
Let S identify the lower-rate class and let N be the observed annual count. Record the prior probabilities and the zero-count likelihoods.
Model
Apply Bayes' theorem using the zero observation as the evidence.
Compute
Substitute the two Poisson likelihoods and prior class weights.
Answer
The posterior probability rounds to 0.52.
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Original practice · fully worked
A shipment arrives from either North Dock or South Dock. A scan flags 20% of North Dock shipments and 50% of South Dock shipments. Among flagged shipments, the probability of North Dock origin is 1/3. Calculate the prior probability that a shipment comes from North Dock.
Writing the unknown prior as p and applying Bayes gives 0.2p/[0.2p+0.5(1-p)]=1/3. Solving yields p=5/9, so choice D is correct.
Setup
Let p be the unknown prior probability of North Dock origin and let F denote a scan flag.
Model
Express the supplied posterior probability in terms of the unknown prior.
Compute
Cross-multiply and solve the resulting linear equation.
Answer
The North Dock prior probability is five-ninths.
Keep practicing
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 Poisson Distribution problems
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ActuaryProof. “SOA Exam P Sample Question #572 — Verified Solution.” Verified 2026-07-30.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-30.
