|Binomial probability is the study of things that can only happen in two possible ways:
heads or tails
on or off
zero or one
black or white
pass or fail
left or right
Many things studied in statistics are of this simple binomial type. Sometimes things that are binomial (only two possibilities) can be combined. A simple example is to toss two coins. The coins can only land heads or tails, but because you have two coins, your possible answers (the sample space) are more complicated. You can get 2 heads, 2 tails, or one of each. In fact, if you do this many times you will get twice as many of the one of each combination as you get for both heads or both tails.
Binomial probability studies all the ways you can combine simple 2 answer probabilities. You can imagine it gets very complicated if you try to figure out all the possibilities when you toss 10 coins or even 20 coins. You still only have heads or tails, but there are a huge number of different ways you can get an answer.
If you have every watched "The Price is Right" on television you might realize that the Plinko game is an example of a binomial distribution. For every level the Plinko disk drops, it hits a peg and it can only go either left or right. The number of possible ways the disk can make it to the bottom depends on the number of layers. Using a statistical point of view, you should always start from the exact center of the Plinko game for the best chances of winning. If you have watched the show, you know that the contestants rarely start at the middle. This is an example of the difference you get in results when doing something a few times (only one or two Plinko chips) and doing it thousands of times (a statistician using computer simulations).
Some early work with the binomial distribution was done by Blaise Pascal, and one tool that bears his name is Pascal's triangle.
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