Verified solution · Exam P
This Exam P sample reference tests Geometric Distribution. This is a geometric waiting-time probability. One experiment succeeds on either of two all-matching outcomes, so its success probability is 1/4; two failures followed by a success have probability (3/4)²(1/4)=9/64, or 0.140625 and choice C.
Independent solution
Setup
Count the two qualifying configurations among the eight equally likely outcomes of one experiment.
Model
A first success on experiment three requires failures on experiments one and two, then success on experiment three.
Compute
Multiply the independent experiment-level probabilities.
Answer
The probability rounds to 0.141.
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Original practice · fully worked
Uploaders A and B make one independent transmission attempt per round until their own first success. Each A attempt succeeds with probability 0.25, and each B attempt succeeds with probability 0.50. Calculate the probability that uploader A succeeds in a strictly earlier round than uploader B.
If A first succeeds in round k while B remains unsuccessful through that round, the probability is 0.25(0.50)(0.75 × 0.50)⁽ᵏ⁻¹⁾. Summing the geometric series gives 0.125/(1-0.375)=0.20, so choice B.
Setup
Let T_A and T_B be the two independent geometric completion rounds.
Model
For A to win in round k, both uploaders must fail each earlier round, then A succeeds while B fails in round k.
Compute
Sum over every possible winning round.
Answer
Uploader A finishes strictly first with probability 0.200.
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ActuaryProof. “SOA Exam P Sample Question #303 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
