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

• A. The probability of success must increase with each trial.
• B. The number of trials can vary depending on the outcome of previous trials.
• C. Each trial has only two possible outcomes, commonly called $\mathrm{success}$ and $\mathrm{failure}$.
• D. Each trial must have a different probability of $\mathrm{success}$.

Answer: (C)

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 of the others, (3) Each trial has only two possible outcomes, often called success and failure, and (4) The probability of success remains constant for each trial.
3. Evaluate each option against these criteria: The probability of success must NOT increase with each trial; it should remain constant. The number of trials should be fixed, not vary depending on previous outcomes. Each trial must have only two possible outcomes. The probability of success must be the same for each trial, not different.
4. Identify that the correct criterion is the one stating that each trial has only two possible outcomes, commonly called success and failure, because this matches the third key criterion of a binomial experiment.
5. Conclude that the other options violate the fundamental properties of a binomial experiment and therefore are not correct criteria.