Which of the following is a property of binomial distributions?

• A. The outcomes of different trials are always dependent.
• B. The number of trials can be $\mathrm{infinite}$.
• C. Each trial has only $2$ possible outcomes, often called success and failure.
• D. The probability of success changes from trial to trial.

Answer: (C)

Verified step by step guidance

1. Understand that a binomial distribution models the number of successes in a fixed number of independent trials.
2. Recall the key properties of a binomial distribution: each trial is independent, there are a fixed number of trials, each trial has only two possible outcomes (success or failure), and the probability of success remains constant across trials.
3. Evaluate each given statement against these properties: outcomes being dependent contradicts independence; infinite trials contradicts the fixed number of trials; probability changing contradicts the constant probability assumption.
4. Identify that the correct property is that each trial has only two possible outcomes, often called success and failure, which aligns with the definition of a binomial distribution.
5. Summarize that the binomial distribution requires independent trials, fixed number of trials, two possible outcomes per trial, and constant probability of success.