A binomial distribution is a statistical model that describes the number of successes in a fixed number of independent trials, each with the same probability of success. It is commonly used in scenarios where there are two possible outcomes, such as success or failure. The distribution is defined by two parameters: the number of trials (n) and the probability of success (p). In a binomial distribution, the probability of obtaining exactly k successes in n trials can be calculated using the formula: P(X = k) = (n choose k) * p^k * (1-p)^(n-k). This model is useful in various fields, including biology, finance, and quality control, to analyze outcomes and make predictions based on probabilities.