Which of the following is a criterion for a binomial probability experiment?

• A. Each trial has only two possible outcomes, commonly called $\mathrm{success}$ and $\mathrm{failure}$.
• B. The probability of $\mathrm{success}$ must change from trial to trial.
• C. The number of trials can vary depending on the outcome of previous trials.
• D. Each trial must have more than two possible outcomes.

Answer: (A)

Verified step by step guidance

1. Understand that a binomial probability experiment is a specific type of experiment with certain criteria that must be met.
2. Recall the key criteria for a binomial experiment: (1) The experiment consists of a fixed number of trials, (2) Each trial is independent, (3) Each trial has only two possible outcomes, often called success and failure, and (4) The probability of success remains constant across trials.
3. Evaluate each option against these criteria: The correct criterion is that each trial has only two possible outcomes (success and failure).
4. Note that the probability of success must NOT change from trial to trial; it should remain constant for a binomial experiment.
5. Also, the number of trials should be fixed in advance and not vary depending on previous outcomes, and each trial should not have more than two possible outcomes.