Probability and Binomial distribution are some of the building blocks to the development of statistical inference on a population of interest. The Binomial distribution is a discrete distribution, i.e., the probability distribution for discrete data, was developed from probability theory. A distribution may look awkward at first sight, but we need it in order to draw inference on the population of interest. For example, the Binomial distribution can be used for estimating the proportion of hypertensive patients in Hong Kong, or the response rate of a treatment.
The key characteristics of a Binomial distribution are (i) it models the "sum" of a series of independent events, (ii) each event can either be "success" or "failure"; (iii) the occurrence of an event does not influence the chance of occurrence of the other events. Apart from the coin flipping example, another example can be the throwing of a die (6-faces). Suppose we throw the die ten times, and we are interested in counting the number of times we have a number below 3. Then (i) the "sum" corresponds to the number of times we have a number below 3 out of the ten tosses; (ii) the "event" is either a number below 3 or a number above 3; (iii) the number obtained from one toss does not affect the results from other tosses.