Suppose an experiment conforms to the following requirements: (1) the experiment consists of
is fixed before the start of the experiment; (2) the trials are independent Bernoulli experiments (i.e., each trial results in either a success or failure); (3) the trials are independent, so that the outcome of any particular trial does not influence the outcome of any other trial; and (4) the probability of success is constant from trial to trial and is denoted by
. An experiment that satisfies conditions (1) to (4) is called a binomial experiment. Given a binomial experiment consisting of
trials, the probabilities that the binomial random variable
associated with this experiment takes on values in its range can be found using the binomial probability function
. This Demonstration shows these probabilities for a user-specified value of the number of trials or experiments and the probability of success for a trial.