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 must have a different probability of success.
• D. Each trial has only two possible outcomes, commonly called $\mathrm{success}$ and $\mathrm{failure}$.

Answer: (D)

Verified step by step guidance

1. Understand that a binomial probability experiment is a specific type of probability 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 has only two possible outcomes, often called success and failure, (3) The probability of success is the same for each trial, and (4) The trials are independent of each other.
3. Evaluate each given option against these criteria: For example, the probability of success must remain constant (not increase), the number of trials must be fixed (not vary), and each trial must have the same probability of success (not different).
4. Identify that the correct criterion among the options is that each trial has only two possible outcomes, commonly called success and failure, which aligns with the second key criterion of a binomial experiment.
5. Conclude that the other options violate the fundamental properties of a binomial experiment, so the correct answer is the one stating the two possible outcomes per trial.