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Which set of three conditions must a statistical experiment satisfy to be classified as binomial?
AFixed trials, outcomes counted until first success, no replacement
BUnlimited trials, two groups sampled, dependent draws
CFixed trials, two outcomes with constant p and q, independent trials
DFixed trials, outcomes in a time interval, known average rate
Answer & Solution
Correct answer: C. Fixed trials, two outcomes with constant p and q, independent trials
1. A binomial experiment has a fixed number of trials, n.
2. Each trial has exactly two outcomes, success and failure, with constant probabilities p and q where p + q = 1.
3. The n trials must also be independent, run under identical conditions.
4. Option A describes a geometric experiment and option D describes a Poisson experiment, so neither is binomial.
_Source: OpenStax Introductory Statistics (CC BY 4.0), Ch 4 "Discrete Random Variables", section 4.3 Binomial Distribution_
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