Verified solution · Exam P
This Exam P sample reference tests Conditional Probability. The under-25 group has size 505. Its female portion is 0.57(414)=235.98, leaving 269.02 males, so the requested conditional probability is 269.02/505=0.5327, choice B.
Independent solution
Setup
Split the portfolio by sex and by whether age exceeds the cutoff.
Model
Within the female group, the probability of being at or below the cutoff is the complement of the supplied older-age probability.
Compute
Subtract the female portion from the full under-25 group and condition on that group.
Answer
The conditional male proportion rounds to 0.53.
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Error diagnosis
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Original practice · fully worked
A component inventory comes 40% from supplier A, 35% from supplier B, and 25% from supplier C. Defect rates are 2% for A and 4% for B, while the inventory-wide defect rate is 3.25%. A nondefective component is selected. Determine the probability that it came from supplier C.
The mixture defect rate implies supplier C has defect rate 0.042. Its nondefective mass is 0.25(0.958)=0.2395, and dividing by the total nondefective mass 0.9675 gives 0.2475, choice C.
Setup
Let q be the unknown defect probability for supplier C.
Model
Solve the mixture equation and complement the resulting supplier-specific defect rate.
Compute
Apply Bayes' rule to the nondefective selection.
Answer
About 24.75% of accepted components come from supplier C.
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ActuaryProof. “SOA Exam P Sample Question #132 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
