Which statement about binomial trials is true?

Which statement about binomial trials is true?

• A. The probability of success is constant across trials
• B. The trials are dependent
• C. The number of trials is not fixed
• D. There are more than two outcomes

Answer: (A)

In a binomial setup, you perform a fixed number of independent trials, and each trial has the same probability of success. The key point is that this probability does not change from one trial to the next, so every trial is a Bernoulli trial with the same p. This sameness of p across trials is what defines the binomial model and leads to the distribution of the number of successes as Bin(n, p). Because of that fixed, identical probability, the statement that the probability of success is constant across trials is the correct one. The other statements don’t fit: if trials were dependent, you wouldn’t have a binomial distribution; if the number of trials weren’t fixed, you’d be outside the binomial framework; and binomial trials have two outcomes, not more than two. For intuition, think of flipping a fair coin a predetermined number of times—the chance of heads is constant on every flip, and the total number of heads across all flips follows a binomial distribution.

In a binomial setup, you perform a fixed number of independent trials, and each trial has the same probability of success. The key point is that this probability does not change from one trial to the next, so every trial is a Bernoulli trial with the same p. This sameness of p across trials is what defines the binomial model and leads to the distribution of the number of successes as Bin(n, p).

Because of that fixed, identical probability, the statement that the probability of success is constant across trials is the correct one. The other statements don’t fit: if trials were dependent, you wouldn’t have a binomial distribution; if the number of trials weren’t fixed, you’d be outside the binomial framework; and binomial trials have two outcomes, not more than two. For intuition, think of flipping a fair coin a predetermined number of times—the chance of heads is constant on every flip, and the total number of heads across all flips follows a binomial distribution.