Which of the following is not a requirement of the binomial probability distribution?

• A. There is a fixed number of trials.
• B. The probability of success is the same for each trial.
• C. Each trial has more than $2$ possible outcomes.
• D. The trials are independent.

Answer: (C)

Verified step by step guidance

1. Step 1: Understand the binomial probability distribution. It models the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes: success or failure.
2. Step 2: Identify the key requirements of a binomial distribution: (a) There is a fixed number of trials, (b) Each trial is independent, (c) The probability of success is the same for each trial, and (d) Each trial results in exactly two possible outcomes.
3. Step 3: Analyze the given options to see which one does not fit these requirements. The option 'Each trial has more than two possible outcomes' contradicts the requirement that each trial must have exactly two outcomes.
4. Step 4: Conclude that the option stating 'Each trial has more than two possible outcomes' is not a requirement of the binomial distribution because it violates the fundamental condition of having only two possible outcomes per trial.
5. Step 5: Summarize that the binomial distribution requires fixed trials, constant success probability, independence, and exactly two outcomes per trial, so any condition outside these is not a requirement.