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

• A. Each trial must have a different probability of success.
• B. The probability of success must increase with each trial.
• C. Each trial results in exactly $2$ possible outcomes, commonly referred to as success and failure.
• D. The number of trials can be infinite.

Answer: (C)

Verified step by step guidance

1. Understand that a binomial probability experiment is defined by specific criteria that must be met for the binomial model to apply.
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 option against these criteria: The probability of success must be constant (not different or increasing), the number of trials must be fixed (not infinite), and each trial must have exactly two possible outcomes.
4. Identify that the correct criterion is that each trial results in exactly two possible outcomes, commonly referred to as success and failure, because this matches the second key criterion of a binomial experiment.
5. Conclude that the other options do not satisfy the binomial experiment conditions, so the correct answer is the one stating the two possible outcomes per trial.