If an experiment generates only two results and measures the likelihood of an occurrence happening when a fixed number of experiments are used, a binomial distribution is used. When a discrete likelihood distribution exists, in each case only two mutually excluded outcomes (only two options) exist (Bluman, Allan G). These two findings are generally referred to as success and failure. The experiments carried out are often mutually independent. The binomial distribution is essentially a statistical instrument used to assess the likelihood of success frequency in a fixed number of studies. Certain conditions have to be met to classify a variable as a binomial random variable. They are:
1) Number of trials is already set, that is it is fixed and doesn’t change as trials are conducted
2) For every trial, one of the events of interest must occur.
3) There is an equal probability of occurrence of an event. For example probability of success is fixed in each trial.
4) Trials should be independent of each other
Example of application of binomial distribution can be to find the probability of getting head 5 times when a coin is flipped 10 times. Here the number of trials is fixed i.e. 10, on each trail either head occurs or not, the probability of occurrence of a head in each flip does not change and all the flipping of the coins are independent of each other. Thus it satisfies all the conditions of a binomial random variable. Consequently, the binomial distribution is applicable in the above example to calculate the probability of getting a head 5-times in 10 trails.
Other examples of applications of binomial variable:
The occurrence of odd or even numbers when a dice is thrown.
Defective or non-defective items in a lot.
Success or failure in an experiment.
Male or female in a population.
True or false in an objective test.
Bluman, Allan G. Elementary Statistics: A Step by Step Approach-A Brief Version, 6th Edition McGraw-Hill, 2013. Print.