Verified solution · Exam P
This Exam P sample reference tests Independence. The husband's two-year survival probability is 0.90. Independence makes the joint survival probability the product of the two marginal survival probabilities, so the wife's survival probability is 7/9 and her death probability is 2/9, approximately 0.222. This is choice E.
Independent solution
Setup
Write the husband's survival probability as the complement of his death probability.
Model
For independent survival events, the probability that both spouses survive is the product of their marginal survival probabilities.
Compute
Recover the wife's survival probability, then take its complement.
Answer
The wife's two-year death probability is approximately 0.222.
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Original practice · fully worked
Two backup communication links fail independently during a stress test. Their failure probabilities are 0.08 and 0.15. Given that at least one link fails, calculate the probability that both links fail.
Independence gives a double-failure probability of 0.012, while inclusion–exclusion gives 0.218 for at least one failure. Their ratio is approximately 0.055, choice B.
Setup
Multiply the marginal failure probabilities to obtain the double-failure probability.
Model
Use inclusion–exclusion for the event that at least one link fails.
Compute
Condition the double-failure event on the union of the two failure events.
Answer
Given at least one failure, the probability that both links fail is approximately 0.055.
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ActuaryProof. “SOA Exam P Sample Question #369 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
