Verified solution · Exam P
This Exam P sample reference tests Sampling Without Replacement. This is a without-replacement complement calculation. The probability that both selected units come from the five non-target units is (5/9)(4/8), so the probability of selecting at least one of the four target units is 1-5/18=13/18, approximately 0.722 and choice E.
Independent solution
Setup
Separate the nine units into four target units and five non-target units.
Model
The complement of selecting at least one target unit is selecting two non-target units.
Compute
Because sampling is without replacement, the second non-target probability changes after the first selection.
Answer
The probability rounds to 0.72.
Continue without hunting through PDFs
The searchable 3108-page manual includes this complete solution, its error analysis, and one original worked variant for every active reference.
Error diagnosis
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
Original practice · fully worked
An archive has ten sealed reports: four concern the north region, three concern the south region, and three concern the central region. Three reports are selected uniformly without replacement. Calculate the expected number of different regions represented in the selection.
Use one indicator for whether each region appears. The north is absent in C(6,3)/C(10,3) of selections, while each three-report region is absent in C(7,3)/C(10,3). Adding the three appearance probabilities gives 2.25, choice D.
Setup
Let I_N, I_S, and I_C indicate whether the north, south, and central regions appear, respectively.
Model
A region is absent exactly when all three reports are drawn from the other regions.
Compute
Apply linearity of expectation to the three appearance indicators.
Answer
The selection represents 2.25 regions on average.
Keep practicing
These references share syllabus concepts or sit nearby in the official sequence. All 192 Exam P general probability practice problems.
Continue in syllabus order
The 3108-page Probability Proof Manual reorganizes 718 verified Exam P solutions by syllabus skill and adds formula proofs, error patterns, and original worked practice.
ActuaryProof. “SOA Exam P Sample Question #304 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
