Verified solution · Exam P
This Exam P sample reference tests Binomial Distribution. The binomial masses at zero, one, and two are 0.13262, 0.27065, and 0.27341. Normalizing the exactly-two mass by their sum gives 0.40405, choice D.
Independent solution
Setup
Let X be the binomial defect count and write the requested conditional ratio.
Model
Evaluate the three binomial masses admitted by the conditioning event.
Compute
Normalize the exactly-two mass within the lower-tail event.
Answer
The conditional probability rounds to 0.404.
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Original practice · fully worked
A flagged-item count X has a binomial distribution with unknown size n and success probability p. Its mean is 3 and its variance is 2.1. Calculate the probability that X is zero.
For a binomial count, Var(X)/E[X]=1-p, so p=0.30 and n=10. Therefore P(X=0)=0.70¹⁰=0.02825, choice A.
Setup
Write the binomial mean and variance equations.
Model
Divide the variance by the mean to recover the failure probability.
Compute
Recover the binomial size and evaluate the zero-count mass.
Answer
The probability of zero flagged items is approximately 0.02825.
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Drill the method: Exam P Conditional Probability problems
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Source reference: official SOA sample-question PDF. Last reviewed 2026-07-31.
