Verified solution · Exam P
This Exam P sample reference tests Binomial Distribution. This is a binomial probability-ratio problem. The zero-to-one mass relation gives failure-to-success odds of 60, and the zero-to-three mass ratio is therefore 60³ divided by 20, or 10,800, so choice E is correct.
Independent solution
Setup
Let p be the common disease probability and q=1-p. Write the binomial masses at zero and one.
Model
Translate the first probability comparison into an odds equation.
Compute
Form the requested multiplier by dividing the zero-disease mass by the three-disease mass.
Answer
The zero-disease probability is 10,800 times the three-disease probability.
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Original practice · fully worked
The number X of modules that pass a production diagnostic follows a binomial distribution with unknown trial count and success probability. Historical batches give E[X]=4.8 and Var(X)=1.92. Calculate the probability that at least six modules pass in the next batch.
Dividing the variance by the mean gives failure probability 0.40, so the success probability is 0.60 and the trial count is eight. The binomial upper tail from six through eight is 0.31539456, selecting choice D.
Setup
Let the binomial parameters be n and p and write its mean and variance equations.
Model
Use the ratio of variance to mean to identify p, then recover the integer trial count.
Compute
Add the three binomial masses that satisfy the requested upper-tail event.
Answer
The probability of at least six passing modules is approximately 0.3154.
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ActuaryProof. “SOA Exam P Sample Question #608 — Verified Solution.” Verified 2026-07-30.
Source reference: official SOA sample-question PDF. Last reviewed 2026-07-30.
