Verified solution · Exam P
This Exam P sample reference tests Survival Functions. A unit survives through the second-year endpoint with probability 2⁻¹⁄⁴. Independence makes the three-unit no-failure probability 2⁻³⁄⁴, so the expected 1000 payment is 1000(1-2⁻³⁄⁴)=405.396 and choice C.
Independent solution
Setup
Let T_i be the failure age of unit i. The supplied distribution gives the survival probability through age 2 directly.
Model
The payment indicator is one unless every unit avoids failure during the covered year.
Compute
Use independence, take the complement, and multiply by the fixed benefit.
Answer
The expected payment is approximately 405.
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Original practice · fully worked
Four sensors are calibrated independently and have a common probability p of producing an acceptable reading. The probability that all four readings are acceptable is 0.4096. A batch is discarded when at least two readings are unacceptable. Calculate the discard probability.
The all-acceptable probability gives p⁴=0.4096 and hence p=0.80. For K, the number unacceptable, P(K≥2)=1-P(K=0)-P(K=1)=1-0.4096-0.4096=0.1808, so choice B.
Setup
Recover the one-sensor acceptable probability from the four-sensor joint probability.
Model
Let K count unacceptable readings. The discard event is K at least two, whose complement contains K=0 and K=1.
Compute
Evaluate the two complement terms using p=0.80.
Answer
The batch-discard probability is 0.1808.
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ActuaryProof. “SOA Exam P Sample Question #496 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
