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

• A. There is a fixed number of trials.
• B. The trials are dependent on each other.
• C. The probability of success remains constant for each trial.
• D. Each trial has exactly two possible outcomes, commonly called success and failure.

Answer: (B)

Verified step by step guidance

1. Step 1: Understand the binomial distribution requirements. The binomial distribution models the number of successes in a fixed number of independent trials.
2. Step 2: Identify the key requirements: (a) There is a fixed number of trials, denoted by \(n\); (b) Each trial has exactly two possible outcomes, often called success and failure; (c) The probability of success, denoted by \(p\), remains constant for each trial; (d) The trials are independent of each other.
3. Step 3: Analyze the given options to see which one violates these requirements. The option stating "The trials are dependent on each other" contradicts the independence requirement.
4. Step 4: Recall that dependence between trials means the outcome of one trial affects the others, which is not allowed in a binomial setting.
5. Step 5: Conclude that the statement "The trials are dependent on each other" is not a requirement of the binomial distribution; in fact, it is the opposite of what is required.