Verified solution · Exam P
This Exam P sample reference tests Bayes' Theorem. This is a Bayes calculation using committee membership as the partition. Committee Y contributes 0.36 to the male probability, and the two committees contribute 0.48 in total. The posterior share from Y is therefore 0.75, choice E.
Independent solution
Setup
Complement the supplied female rate within committee Y and the committee-Y marginal.
Model
Compute the male contributions from the two committees.
Compute
Normalize committee Y's contribution by the total male probability.
Answer
Given that the person is male, the probability of committee Y is 0.75.
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Original practice · fully worked
A quality inspector selects crate A with probability 0.40 and crate B with probability 0.60. Crate A contains three silver and one black component; crate B contains two silver and two black components. Two components are drawn without replacement from the selected crate and both are silver. Calculate the conditional probability that crate A was selected.
The prior-weighted probabilities of drawing two silver components are 0.20 for crate A and 0.10 for crate B. Crate A therefore supplies two thirds of all such draws, choice E.
Setup
Calculate the probability of two silver components under each crate.
Model
Weight each likelihood by its crate-selection probability.
Compute
Normalize crate A's contribution by the total evidence probability.
Answer
The posterior probability of crate A is two thirds.
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ActuaryProof. “SOA Exam P Sample Question #359 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
