The binomial distribution is a discrete probability distribution that summarizes the probability of the number of successes in a sequence of n independent experiments, each with its own Boolean-valued outcome: success (with probability p) or failure (with probability q = 1 - p) . A single success/failure experiment is also called a Bernoulli trial or Bernoulli experiment, and a sequence of outcomes is called a Bernoulli process. The binomial distribution is frequently used to model the number of successes in a sample of size n drawn with replacement from a population of size N. The binomial distribution formula is for any random variable X, given by:

$$P(x:n,p) = nC_x p^x (1-p)^{n-x}$$

where n is the number of experiments, p is the probability of success in a single experiment, q is the probability of failure in a single experiment (= 1 – p), and takes values as 0, 1, 2, 3, 4, …, n. The binomial distribution is the sum of a series of multiple independent and identically distributed Bernoulli trials. The binomial distribution is a common discrete distribution used in statistics, as opposed to a continuous distribution, such as the normal distribution. The binomial distribution is used to determine the probability of observing a specific number of successful outcomes in a specified number of trials. The binomial distribution is the discrete probability distribution that gives only two possible results in an experiment, either success or failure. The binomial distribution is the base for the famous binomial test of statistical importance. The binomial distribution is used in various real-life scenarios, such as taking a survey of positive and negative reviews from the public for any specific product or place, checking whether the number of persons views a particular channel, and finding the probability of getting heads when a coin is tossed n times.