Worked solution · Exam P

SOA Exam P Sample Question #6 Solution

This Exam P sample reference tests Conditional Probability. There are 625 records without the parental condition and 108 relevant deaths among them, giving 108/625=0.1728, choice B.

Independent analysis by ActuaryProof · reviewed July 31, 2026

Official wording withheld. Read the problem in the official SOA sample-question PDF. This page provides only our independently written analysis.

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Independent solution

How to solve this Conditional Probability question

Setup

Form the conditioning group F complement by subtracting the 312 records in F from the total of 937.

N(F^c)=937-312=625

Model

The numerator must count records in H but not F, so subtract the 102 records in both H and F from the 210 records in H.

N(H\cap F^c)=210-102=108

Compute

There are 108 qualifying H records among 625 records in F complement; their ratio is 108/625=0.1728.

\Pr(H\mid F^c)=\frac{108}{625}=0.1728

Answer

Rounding the conditional probability to three decimals gives 0.173, which is choice B.

\boxed{0.173\quad\text{(B)}}

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Error diagnosis

Why the other letters tempt

These notes identify the calculation error associated with each wrong letter when that error is reproducible.

AThe value 0.115 is 108/937. It uses the full population as denominator instead of conditioning on the 625 records outside F.
CThe value 0.224 is 210/937, the unconditional proportion in H rather than Pr(H given F complement).
DThe value 0.327 is 102/312, the conditional proportion Pr(H given F); it conditions on F instead of its complement.

Original practice · fully worked

Original variant: infer a segment rate from the portfolio average

Forty percent of a portfolio consists of newly issued contracts, whose event rate is 0.12. The remaining contracts are seasoned. The whole portfolio has event rate 0.18. Determine the event rate among seasoned contracts.

A
0.120
B
0.180
C
0.220
D
0.240
E
0.300

Answer and calculation

The portfolio rate is a two-segment weighted average. Solving 0.18=0.40(0.12)+0.60s gives s=0.22, choice C.

Setup

Let s be the event rate among seasoned contracts; the new and seasoned portfolio shares are 0.40 and 0.60.

s=\Pr(E\mid\text{seasoned})

Model

Express the overall event rate as the weighted average of the two segment-specific rates.

0.18=0.40(0.12)+0.60s

Compute

The new-contract contribution is 0.40(0.12)=0.048, leaving 0.132 for seasoned contracts; division by 0.60 gives s=0.22.

0.132=0.60s,\qquad s=0.22

Answer

The seasoned-contract event rate is 0.220, so the correct answer is choice C.

\boxed{0.22\quad\text{(C)}}

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How to solve this Conditional Probability question

Setup

Model

Compute

Answer

General Probability Practice Workbook

Why the other letters tempt

Original variant: infer a segment rate from the portfolio average

Answer and calculation

Setup

Model

Compute

Answer

Related Exam P solutions

Next steps for Exam P General Probability