$$Which of the following is not a requirement of the binomial probability distribution?$$

• A. $$Each trial results in only two possible outcomes: success or failure.$$
• B. $P(success)$ can change from trial to trial.
• C. $$There must be a fixed number of trials.$$
• D. $$Each trial must be independent of the others.$$

Answer: (B)

Verified step by step guidance

1. Understand that the binomial probability distribution models the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes: success or failure.
2. Recall the key requirements of a binomial distribution: (1) Each trial results in only two possible outcomes (success or failure), (2) The number of trials, denoted by \(n\), is fixed in advance, (3) Each trial is independent of the others, and (4) The probability of success, denoted by \(p\), remains constant for each trial.
3. Analyze the given options and identify which one contradicts these requirements. Specifically, check if the probability of success changes from trial to trial, which would violate the assumption of a constant probability \(p\).
4. Conclude that the statement 'The probability of success can change from trial to trial' is not a requirement of the binomial distribution; in fact, it is a condition that must not happen for the binomial model to apply.
5. Summarize that all other options are true requirements of the binomial distribution, while the changing probability of success is not.