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An ABC College committee of ten staff and six students draws two names without replacement, one becomes chairperson and the second becomes recorder. Why is this NOT a binomial experiment?
AThere are more than two possible outcomes per trial
BThe number of trials is not fixed in advance
CDrawing without replacement violates the independence condition
DThe probability of success is unknown before drawing
Answer & Solution
Correct answer: C. Drawing without replacement violates the independence condition
1. There are two trials here (drawing a chairperson, then a recorder), and each trial has exactly two outcomes, student or staff.
2. Because names are drawn without replacement, the probability of drawing a student on the second trial depends on what happened on the first.
3. That dependence breaks the independence condition that a binomial experiment requires.
4. Options A, B, and D describe conditions that actually do hold here, so they are not the reason this fails to be binomial.
_Source: OpenStax Introductory Statistics (CC BY 4.0), Ch 4 "Discrete Random Variables", section 4.3 Binomial Distribution_
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