The binomial distribution is a probability distribution that describes the number of successes in a fixed number of independent Bernoulli trials, where each trial has two possible outcomes: success (often denoted as 1) and failure (denoted as 0). The probability of success is constant across trials. For example, flipping a coin multiple times is a classic scenario that follows a binomial distribution, where heads can be considered a success and tails a failure ³.

In a binomial experiment, the outcomes of each trial are independent of one another. This means that the result of one trial does not affect the results of others. The binomial distribution can be characterized by two parameters: the number of trials (N) and the probability of success (p) in each trial. The distribution can be used to calculate the probability of obtaining a specific number of successes in those trials ²⁴.

The binomial probability mass function (PMF) and cumulative density function (CDF) are commonly used to compute probabilities associated with the binomial distribution. The PMF gives the probability of observing exactly k successes in N trials, while the CDF provides the probability of observing up to k successes ³.