Binomial Distribution

The binomial distribution is a discrete probability distribution that gives the probability of obtaining a fixed number of successes in a fixed number of independent trials, each of which has only two possible outcomes and the same probability of success. It is characterized by two parameters, the number of trials and the probability of success on each individual trial, and its name comes from the binomial coefficients that appear in its formula, the same coefficients that appear in the algebraic expansion of a two term expression raised to a power. The distribution was first derived by Jacob Bernoulli, and it is one of the oldest and most widely used discrete distributions in statistics, applied whenever an experiment can be modeled as a fixed number of repeated yes or no trials, such as counting heads in a series of coin flips or defective items in a batch of manufactured parts.