Verified solution · Exam P

SOA Exam P Sample Question #296 Solution

This Exam P sample reference tests Contingency Tables. Express the four portfolio cells using one male-nonsmoker count and the unknown female-smoker count. The stated total and row differences reduce to 100=2y, so there are 50 female-smoker policies 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 Contingency Tables question

Setup

Let x be the male-nonsmoker count and y the requested female-smoker count.

MN=x,\qquad FN=x+100

FS=y,\qquad MS=350-y

Model

Form the male and female portfolio totals from the four cells.

M=x+350-y

F=x+100+y

Compute

Apply the stated excess of male policies over female policies and solve.

x+350-y=(x+100+y)+150

100=2y,\qquad y=50

Answer

The number of female-smoker policies is 50.

\boxed{50\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.

BThis reports the intermediate difference 100 from the equation 100=2y and omits division by two.
CThis subtracts the overall male-female excess from the smoker total, 350-150=200, but ignores the opposite 100-policy nonsmoker imbalance.
DThis subtracts the nonsmoker difference directly from the smoker total, 350-100=250. Both row differences must be combined before splitting the smoker total.
EAfter the correct female-smoker count is 50, the male-smoker count is 350-50=300. This choice reports the complementary smoker cell.

Original practice · fully worked

Original variant: premium-kit production count

A workshop assembles 96 sensor kits, each either standard or premium. A standard kit uses two control chips, while a premium kit uses five. The day's completed kits use 330 control chips in total. Calculate the number of premium kits assembled.

A
32
B
46
C
50
D
64
E
110

Variant answer in brief

Let S and P be the standard and premium counts. Subtracting twice the total-kit equation from the chip equation leaves 3P=138, so P=46 and choice B.

Setup

Translate the kit and chip totals into two equations.

S+P=96

2S+5P=330

Model

Remove the two-chip baseline used by every kit.

2S+2P=192

(2S+5P)-(2S+2P)=330-192

Compute

The remaining chips are the three-chip premium increments.

3P=138

P=46

Answer

The workshop assembled 46 premium kits.

\boxed{46\quad\text{(B)}}

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Cite this solution

ActuaryProof. “SOA Exam P Sample Question #296 — Verified Solution.” Verified 2026-07-31.

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

How to solve this Contingency Tables question

Setup

Model

Compute

Answer

All 718 Exam P sample solutions in syllabus order

Why the other letters tempt

Original variant: premium-kit production count

Variant answer in brief

Setup

Model

Compute

Answer

Related Exam P solutions

Turn this solution into a complete study sequence

Cite this solution