Suppose an experiment has only 2 possible outcomes, “success” (outcome you are interested in observing) or “failure” (the other outcome). The probability of a “success” is p and the probability of a “failure” is 1 – p. Furthermore suppose the experiment is repeated n times (n trials) in such a way that the probability of success remains the same for each trial and the outcome of each trial is independent of the other trials.
Define a random variable X = number of successes
The random variable X is said to be a Binomial Random Variable.
Notation: X ~ B(n, p).