Binomial distribution
In probability theory and statistics, the
binomial distribution is the discrete probability distribution of the number of successes in a sequence of
n independent yes/no experiments, each of which yields success with probability
p. Therewith the probability of an event is defined by its binomial distribution. A success/failure experiment is also called a Bernoulli experiment or Bernoulli trial; when
n = 1, the binomial distribution is a Bernoulli distribution. The binomial distribution is the basis for the popular binomial test of statistical significance. 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. If the sampling is carried out without replacement, the draws are not independent and so the resulting distribution is a hypergeometric distribution, not a binomial one. However, for
N much larger than
n, the binomial distribution is a good approximation, and widely used.