Binomial Distribution: The binomial distribution, also known as Bernoulli distribution, describes the random sampling processes that all outcomes are either yes or no (success/failure) without ambiguity. In addition, the probability will not change from one trial to another (independent). See plots of binomial distributions.
Hypergeometric Distribution: The hypergeometric distribution describes the random sampling processes in which once a sample has been chosen, it will NOT be placed back into the sampling pool (sampling without replacement). In this case, the number of total available samples will decrease by one after each trial. See plots of hypergeometric distributions.
Poisson Distribution: The Poisson distribution describes the random sampling process in which the desired outcomes occur relatively infrequently but at a regular rate. See plots of Poisson distributions.
For further summaries and plots, see the Distributions in Discrete Systems section.