Questions: Which of the following is not a requirement of the binomial probability distribution? Choose the correct answer below. A. The procedure has a fixed number of trials. B. Each trial must have all outcomes classified into two categories. C. The probability of a success remains the same in all trials. D. The trials must be dependent.

Solution Steps

The binomial distribution is defined by a set of specific requirements. These include:

1. A fixed number of trials, denoted as \( n \).
2. Each trial must result in one of two outcomes, typically classified as "success" or "failure".
3. The probability of success, denoted as \( p \), remains constant across all trials.
4. The trials must be independent, meaning the outcome of one trial does not affect the outcome of another.

Given the options:

• A. The procedure has a fixed number of trials. (True)
• B. Each trial must have all outcomes classified into two categories. (True)
• C. The probability of a success remains the same in all trials. (True)
• D. The trials must be dependent. (False)

Among the options, option D states that "the trials must be dependent." This contradicts one of the fundamental properties of the binomial distribution, which requires that the trials be independent.

Final Answer