Verified solution · Exam P
This Exam P sample reference tests Uniform Distribution. The stated moments identify a uniform interval from 7 to 10. Conditioning on survival past 7.5 restricts the possible interval to length 2.5, while continuing past 9 leaves length 1, so the conditional probability is 1/2.5=0.40 and choice B is correct.
Independent solution
Setup
Use the uniform mean and variance to recover the two endpoints.
Model
The interval width is positive, so the moment equations give a width of 3 and an endpoint sum of 17.
Compute
Given that the duration exceeds 7.5, the favorable portion above 9 has length 1 out of a remaining length of 2.5.
Answer
The requested conditional probability is 0.40.
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
Two couriers arrive independently at a loading bay, with each arrival time uniform over the same ten-minute receiving window. Given that at least one courier arrives during the first four minutes, calculate the probability that both couriers arrive during the first six minutes.
The conditioning event occupies probability 0.64. Both arrivals lie before minute six and at least one lies before minute four with probability 0.36-0.04=0.32, so the conditional probability is 0.32/0.64=0.50 and choice C is correct.
Setup
Let U and V be the two independent arrival times, each uniform from zero to ten. Express the condition and target using their minimum and maximum.
Model
Use the complement in which both couriers arrive at or after minute four to find the probability of the conditioning event.
Compute
Within the square where both arrivals are before minute six, remove the smaller square where both fall between minutes four and six.
Answer
The conditional probability is one half.
Keep practicing
These references share syllabus concepts or sit nearby in the official sequence. All 388 Exam P univariate random variables practice problems.
Drill the method: Exam P Conditional Probability problems · Exam P Uniform Distribution 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 #618 — Verified Solution.” Verified 2026-07-30.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-30.
