What is the laymen meaning of "sampling from a binomial distribution"? I know what is binomial distribution but I am not able to realize sampling associated with it. Further a formal statement and applications of sampling from a binomial distribution would be of great help.
Thanks.
 A: Surveys give the best example. Suppose, from a previous survey, it is known that 40% of students at a certain university are in favor of concealed campus carry laws. If you were to do the survey again now, and set out to ask 500 students, you would expect about 200 students to respond in favor. Recall that for a random variable to be distributed as binomial, you must have a fixed number of trials, the same outcomes each time, and independence of trials. We have that here.
A: A Binomial Distribution is that of the count of successes among a certain amount of success/failure trials;† each with an identical and independent rate of success.
So if you have a known amount of trials, $n$, all with the same probability of success, $p$, and each is independent of every other, then the count of successes is a $\mathcal {Bin}(n, p)$ random variable.
Examples:


*

*tossing the same coin a certain amount of times and counting the heads.

*rolling a certain amount of identically balanced dice and counting those showing 6

*drawing balls from an jar with replacement and shaking a certain amount of times, and counting those of a particular colour. 

*drawing cards from a standard deck with replacement and shuffling between draws a certain amount of times and counting the aces drawn.

*and so forth.


Additionally, in some cases taking a representative sample from a significantly large population and counting matches of a particular criteria may be approximated as having a binomial distribution.   Though more accurately the count will have a hypergeometric distribution.

† btw, these are called Bernoulli trials.
