The binomial distribution describes the number of times that a particular event will occur in a sequence of observations. The event is coded binary, assuming values zero and one. The binomial distribution is used when a researcher is interested in the occurrence of an event. For instance, in a clinical trial, a patient may survive or die. The researcher studies the number of survivors, and not how long the patient survives after treatment.
The binomial distribution is specified by the number of observations,denoted by n, and the probability p of occurence. In the graph a binomial distribution with parameters n=10 and p=.20 is shown.
A classic example that is used often to illustrate concepts of probability theory, is the tossing of a coin. If a coin is tossed 4 times, then we may obtain 0, 1, 2, 3, or 4 heads. We may also obtain 4, 3, 2, 1, or 0 tails, but these outcomes are equivalent to 0, 1, 2, 3, or 4 heads. The likelihood of obtaining 0, 1, 2, 3, or 4 heads is, respectively, 1/16, 4/16, 6/16, 4/16, and 1/16.
Other situations in which binomial distributions arise are market research, public opinion surveys,public health, medical research, and animal abundance problems.