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

• A. The number of trials can vary depending on the outcome of previous trials.
• B. Each trial must have more than $2$ possible outcomes.
• C. Each trial results in exactly $2$ possible outcomes, commonly labeled as success and failure.
• D. The probability of success must increase with each trial.

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 results in exactly two possible outcomes, often called success and failure, and (4) The probability of success remains constant for each trial.
3. Analyze each option given in the problem to see if it matches these criteria. For example, if the number of trials can vary depending on previous outcomes, it violates the fixed number of trials condition.
4. Check if the trial outcomes are exactly two. If there are more than two possible outcomes, it does not satisfy the binomial experiment condition.
5. Verify if the probability of success remains constant across trials. If it changes, the experiment is not binomial.