Verified solution · Exam P

SOA Exam P Sample Question #147 Solution

This Exam P sample reference tests Mutually Exclusive Outcomes. The two complement statements identify the endpoint category probabilities as 0.20 each. Subtracting them from the 0.75 lower-stage total leaves 0.35 for the requested category, choice C.

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 Mutually Exclusive Outcomes question

Setup

Let p_j be the probability of category j, where the five category probabilities sum to one.

p_0+p_1+p_2+p_3+p_4=1

Model

Use the two statements that omit one category each to recover those omitted probabilities.

p_1+p_2+p_3+p_4=0.80\implies p_0=0.20

p_0+p_1+p_3+p_4=0.80\implies p_2=0.20

Compute

Subtract the two known category masses from the supplied three-category total.

p_0+p_1+p_2=0.75

p_1=0.75-0.20-0.20=0.35

Answer

The requested category probability is 0.35.

\boxed{0.35\quad\text{(C)}}

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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 0.20 is the probability of either of the two categories recovered directly by complementation, not the requested middle category.
BThe value 0.25 divides the 0.75 three-category total equally, ignoring that two component probabilities are already fixed at 0.20.
DThe value 0.48 cannot satisfy the lower-category equation because 0.20+0.48+0.20=0.88 rather than 0.75.
EThe value 0.65 is impossible once p0=p2=0.20: those three category masses would total 1.05 rather than the supplied 0.75.

Original practice · fully worked

Original variant: recover a route share from pair totals

Each parcel is assigned to exactly one of four routes: North, East, South, or West. The combined shares for North-or-East, East-or-South, and North-or-South are 0.55, 0.60, and 0.45, respectively, while the West share is 0.20. Determine the East share.

A
0.20
B
0.25
C
0.30
D
0.35
E
0.40

Variant answer in brief

Adding the first two pair totals and subtracting the third leaves twice the East share. Thus 2E=0.55+0.60-0.45=0.70 and E=0.35, choice D.

Setup

Translate the three disjoint-route pair totals into equations.

N+E=0.55

E+S=0.60

N+S=0.45

Model

Combine the equations so the North and South shares cancel.

(N+E)+(E+S)-(N+S)=2E

Compute

Evaluate the resulting one-variable equation.

2E=0.55+0.60-0.45=0.70

E=0.35

Answer

The East route receives 35% of parcels.

\boxed{0.35\quad\text{(D)}}

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Cite this solution

ActuaryProof. “SOA Exam P Sample Question #147 — Verified Solution.” Verified 2026-07-31.

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

How to solve this Mutually Exclusive Outcomes question

Setup

Model

Compute

Answer

All 718 Exam P sample solutions in syllabus order

Why the other letters tempt

Original variant: recover a route share from pair totals

Variant answer in brief

Setup

Model

Compute

Answer

Related Exam P solutions

Turn this solution into a complete study sequence

Cite this solution