Verified solution · Exam P
This Exam P sample reference tests Law of Total Probability. Let x be the territory-X share. The overall no-claim rate gives 0.20=0.15x+0.40(1-x), so x=0.80. The no-claim mass from X is then 0.15(0.80)=0.12, and 0.12/0.20=0.60 gives choice D.
Independent solution
Setup
Let x be the prior probability that a policyholder is from territory X, and let N denote no claims.
Model
Use total probability to recover the unknown territory mix.
Compute
Solve for the prior, then apply Bayes' theorem.
Answer
The posterior territory-X probability is 0.60.
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Original practice · fully worked
In a large digital archive, 60% of files use format S and the remaining 40% use format L. The average file sizes are 2 megabytes for format S and 5 megabytes for format L. One stored byte is selected uniformly from all bytes in the archive. Calculate the probability that its containing file uses format L.
Uniform byte sampling weights each file format by both its file share and its average size. The L and S byte-volume weights are 0.40(5)=2.0 and 0.60(2)=1.2, so the L share is 2.0/3.2=0.6250 and choice D.
Setup
Form a byte-volume weight for each format by multiplying file prevalence by average file size.
Model
A uniformly sampled byte belongs to a format in proportion to that format's total byte volume.
Compute
Normalize the L byte-volume weight across both formats.
Answer
The sampled byte comes from format L with probability 0.6250.
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ActuaryProof. “SOA Exam P Sample Question #265 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
