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Why does the outcome of one trial in a binomial experiment fail to help predict the outcome of another trial?
ABecause each trial uses a different value of p
BBecause the number of trials n is unknown
CBecause binomial trials are sampled without replacement
DBecause the trials are independent of one another
Answer & Solution
Correct answer: D. Because the trials are independent of one another
1. Independence is the third defining condition of a binomial experiment.
2. Independent trials mean the result of any one trial carries no information about any other trial's result.
3. That is exactly why one outcome cannot help predict another, matching option A.
4. Options A, B, and D describe conditions that are never attached to binomial independence.
_Source: OpenStax Introductory Statistics (CC BY 4.0), Ch 4 "Discrete Random Variables", section 4.3 Binomial Distribution_
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