Verified solution · Exam P
This Exam P sample reference tests Bayes' Theorem. Prior-weighting the three conditional rates gives total left-handed probability 221/2400. The no-left-handed-parent contribution is 117/2400, so the requested posterior is 117/221=9/17, approximately 0.529 and choice C.
Independent solution
Setup
Complete the three-category prior distribution before conditioning on the child's handedness.
Model
Multiply each family-category prior by its corresponding conditional left-handed rate.
Compute
Normalize the no-left-handed-parent joint weight by the total weight of all left-handed children.
Answer
The posterior probability is about 0.53.
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Original practice · fully worked
One quarter of incoming messages are malicious and the rest are benign. Two filters operate independently after the message type is fixed. Filter 1 alerts on 80% of malicious and 20% of benign messages; Filter 2 alerts on 50% of malicious and 10% of benign messages. A message triggered Filter 1 but not Filter 2. Calculate the probability that it was malicious.
Conditional independence makes the observed alert pattern have likelihood 0.80(0.50)=0.40 for malicious messages and 0.20(0.90)=0.18 for benign messages. Prior-weighting gives masses 0.10 and 0.135, so the malicious posterior is 0.10/0.235=20/47, approximately 0.4255 and choice E.
Setup
Let R denote the mixed result in which the first filter alerts and the second does not.
Model
Multiply the two filter factors within each message type using their stated conditional independence.
Compute
Weight the two likelihoods by their priors and normalize the malicious route.
Answer
The posterior malicious probability rounds to 0.4255.
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ActuaryProof. “SOA Exam P Sample Question #329 — Verified Solution.” Verified 2026-07-31.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
