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

• A. The number of trials can be $\mathrm{infinite}$.
• B. Each trial has only $2$ possible outcomes, commonly called $\mathrm{success}$ and $\mathrm{failure}$.
• C. The probability of $\mathrm{success}$ must change from trial to trial.
• D. The outcomes of each trial must be $\mathrm{dependent}$ on previous trials.

Answer: (B)

Verified step by step guidance

1. Understand that a binomial probability experiment is defined by specific criteria that must all be met for the binomial model to apply.
2. Recall the key criteria for a binomial experiment: (1) The number of trials, \( n \), is fixed and finite; (2) Each trial has only two possible outcomes, often called success and failure; (3) The probability of success, \( p \), remains constant for each trial; (4) The trials are independent, meaning the outcome of one trial does not affect another.
3. Evaluate each option against these criteria: The number of trials cannot be infinite, so the first option is incorrect; the probability of success must remain constant, so the third option is incorrect; the trials must be independent, so the fourth option is incorrect.
4. Identify that the correct criterion is that each trial has only two possible outcomes, commonly called success and failure, which matches the second option.
5. Summarize that the defining feature of a binomial experiment is the binary outcome per trial, fixed number of trials, constant probability of success, and independence of trials.