the theoretical frequency distribution of events that have two possible outcomes.

A random variable has a binomial distribution (with parameters n and p) if it is the number of "successes" in a fixed number n of independent random trials, all of which have the same probability p of resulting in "success." Under these assumptions, the probability of k successes (and n-k failures) is nck pk(1-p)n-k, where nck is the number of combinations of n objects taken k at a time: nck = n!/(K!(N-k)!). The expected value of a random variable with the binomial distribution is n_p, and the standard error of a random variable with the binomial distribution is (n_p_(1 ] - p))_.

A probability distribution for the number of times that an outcome with constant probability will occur in a succession of repetitions of a statistical experiment.

A random variable X has a binomial distribution (X~b(n,p)) if in n independent "trials" with 2 possible outcomes ("success" or "failure") there is a constant probability p of success at each trial. The variable X represents the number of "successes" out of n "trials".

a theoretical distribution of the number of successes in a finite set of independent trials with a constant probability of success

The probability distribution of the total number of successes in a sequence of a fixed number of Bernoulli trials.

"A statistical distribution giving the probability of obtaining a specific number of successes in a binomial experiment" (Borwein, Watters, & Borowski, 1997).

The binomial distribution - Binomial(n, p) - is a probability distribution of the number of successes that occur in independent trials, where the probability of success at any trial is , and the trials are independent ( remains constant). The mean of the distribution is np.

Binomial distributions model (some) discrete random variables. When a coin is flipped, the outcome is either a head or a tail ie there are two mutually exclusive possible outcomes. For convenience, one of the outcomes can be termed 'success' and the other outcome termed 'failure'. If a coin is flipped N times, then the binomial distribution can be used to determine the probability of obtaining exactly r successes in the N outcomes. The formula that is used assumes that the events: fall into only two categories (ie are dichotomous); are mutually exclusive; are independent and are randomly selected.

A distribution usually used for determining confidence for proportions. If there are two possible outcomes, such as either “pass” or “fail” for product tests, or either “heads” or “tails” for coin tosses, then the binomial distribution might be used to estimate the probability of 5 passes and 1 fail in 6 product tests or 2 heads and 2 tails in 4 coin tosses.

The probability distribution that describes the number of successes X observed in n independent trials, each with the same probability of occurrence.

The discrete probability distribution of obtaining exactly n successes out of N trials.

probability distribution that applies to experiments involving sequences of independent trials in which only two possible outcomes (e.g., success or failure) can result on each trial. If is the probability of success on each trial, and the probability of failure, then the probability of success occurring times in trials is given by the binomial distribution

In probability, a binomial distribution gives the probabilities of k outcomes A (or n-k outcomes B) in n independent trials for a two-outcome experiment in which the possible outcomes are denoted A and B.