Is a distribution for the number of successes in a fixed number of Bernoulli trials.

Is a distribution for the number of successes in a fixed number of Bernoulli trials.

• A. Poisson distribution
• B. Binomial distribution
• C. Normal distribution
• D. Uniform distribution

Answer: (B)

The situation described is a classic binomial scenario: you have a fixed number of independent Bernoulli trials, each with the same probability of success p, and you count how many successes occur. This leads to the binomial distribution, where the number of successes X can take values 0, 1, ..., n and has probability mass function P(X = k) = C(n, k) p^k (1−p)^(n−k). The Poisson distribution models counts of events in a fixed interval when events occur at a constant average rate, not when you’re counting a fixed number of trials. The Normal distribution is a continuous approximation that can describe the binomial in some large-sample cases, but it’s not the exact distribution for the described setup. The Uniform distribution would imply every count outcome is equally likely, which isn’t the case here.

The situation described is a classic binomial scenario: you have a fixed number of independent Bernoulli trials, each with the same probability of success p, and you count how many successes occur. This leads to the binomial distribution, where the number of successes X can take values 0, 1, ..., n and has probability mass function P(X = k) = C(n, k) p^k (1−p)^(n−k).

The Poisson distribution models counts of events in a fixed interval when events occur at a constant average rate, not when you’re counting a fixed number of trials. The Normal distribution is a continuous approximation that can describe the binomial in some large-sample cases, but it’s not the exact distribution for the described setup. The Uniform distribution would imply every count outcome is equally likely, which isn’t the case here.