Verified solution · Exam P

SOA Exam P Sample Question #360 Solution

This Exam P sample reference tests Discrete Random Variables. This is an expected surcharge determined by the most recent accident among four independent years. Weighting 20%, 15%, 10%, and 5% by probabilities 0.1, 0.09, 0.081, and 0.0729 gives 0.045245, which rounds to 4.5% and choice A.

Independent analysis by ActuaryProof · reviewed August 4, 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 Discrete Random Variables question

Setup

For each surcharge level, identify the event that its corresponding year is the most recent accident year.

\Pr(J=j)=0.1(0.9)^j,\qquad j=0,1,2,3

Model

Multiply each mutually exclusive event probability by its surcharge rate.

\operatorname{E}[R]=0.20(0.1)+0.15(0.1)(0.9)+0.10(0.1)(0.9)^2+0.05(0.1)(0.9)^3

Compute

Add the four expected-rate contributions.

\operatorname{E}[R]=0.020000+0.013500+0.008100+0.003645

\operatorname{E}[R]=0.045245=4.5245\%

Answer

The expected surcharge rounds to 4.5%.

\boxed{4.5\%\quad\text{(A)}}

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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.

BThe value 5.0% gives every accident-year category probability 0.1 and omits the required accident-free more recent years.
CThe value 8.6% applies an invented flat 25% surcharge whenever any accident occurs, replacing the four stated timing-dependent rates.
DThe value 10.0% repeats the annual accident probability as though it were the expected surcharge rate.
EThe value 19.4% results from swapping the accident and no-accident probabilities when constructing the most-recent-accident events.

Original practice · fully worked

Original variant: nonlinear system-health credit

Four independent monitoring modules each issue an alert with probability 0.20. A system receives a health credit of 30 points if no module alerts, 10 points if exactly one module alerts, and 0 points if two or more modules alert. Calculate the expected health credit.

A
4.096
B
12.288
C
16.384
D
24.576
E
30.000

Variant answer in brief

Zero alerts and exactly one alert each have probability 0.4096. Weighting these outcomes by 30 and 10 points gives an expected credit of 16.384, choice C.

Setup

Let N be the number of modules that alert.

N\sim\operatorname{Binomial}(4,0.20)

Model

Only the zero- and one-alert outcomes make a positive contribution.

\operatorname{E}[C]=30\Pr(N=0)+10\Pr(N=1)

Compute

Evaluate the two binomial probabilities and their weighted sum.

\Pr(N=0)=0.8^4=0.4096

\Pr(N=1)=4(0.2)(0.8)^3=0.4096

\operatorname{E}[C]=30(0.4096)+10(0.4096)=16.384

Answer

The expected health credit is 16.384 points.

\boxed{16.384\quad\text{(C)}}

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Cite this solution

ActuaryProof. “SOA Exam P Sample Question #360 — Verified Solution.” Verified 2026-07-31.

Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.

How to solve this Discrete Random Variables question

Setup

Model

Compute

Answer

All 718 Exam P sample solutions in syllabus order

Why the other letters tempt

Original variant: nonlinear system-health credit

Variant answer in brief

Setup

Model

Compute

Answer

Related Exam P solutions

Turn this solution into a complete study sequence

Cite this solution