Verified solution · Exam P
This Exam P sample reference tests Binomial Distribution. The count is binomial with n=18 and p=0.15. Since (n+1)p=2.85 is not an integer, its unique mode is floor(2.85)=2, so choice C is correct.
Independent solution
Setup
Model the number of positive results as a binomial count.
Model
A binomial distribution has unique mode floor((n+1)p) when (n+1)p is not an integer.
Compute
Take the integer below 2.85.
Answer
The most likely count is 2.
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
The number X of flagged items in ten independent inspections is binomial with an unknown flag probability. The probability of exactly four flags is 1.5 times the probability of exactly three flags. Calculate the mode of X.
The adjacent-mass ratio gives 7p/[4(1-p)]=1.5, so p=6/13. Then (10+1)p=66/13 lies between 5 and 6, making 5 the unique mode and choice C correct.
Setup
Use the ratio of adjacent binomial masses to recover the unknown probability.
Model
Solve the ratio equation for p.
Compute
Apply the binomial mode rule after inferring the parameter.
Answer
The most likely number of flagged items is 5.
Keep practicing
These references share syllabus concepts or sit nearby in the official sequence. All 388 Exam P univariate random variables 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 #592 — Verified Solution.” Verified 2026-07-30.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-30.
