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

• A. Each trial must have exactly $3$ possible outcomes.
• B. There are a fixed number of trials.
• C. Each trial is independent of the others.
• D. The probability of success remains constant for each trial.

Answer: (A)

Verified step by step guidance

1. Understand the binomial probability distribution: it models the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes (success or failure).
2. Identify the key requirements of a binomial distribution: (1) a fixed number of trials, (2) each trial is independent, (3) each trial has exactly two possible outcomes, and (4) the probability of success remains constant for each trial.
3. Analyze the given options and check which one contradicts these requirements. The option stating 'Each trial must have exactly three possible outcomes' conflicts with the binomial distribution's requirement of two outcomes per trial.
4. Confirm that the other options align with the binomial distribution requirements: fixed number of trials, independence of trials, and constant probability of success.
5. Conclude that the statement about three possible outcomes per trial is not a requirement of the binomial probability distribution.