The Binomial Distribution | Probability and Statistics

What is a Binomial Distribution, and how does it work?

A binomial distribution can be thought of as the likelihood of a Positive or FAILURE outcome in a multiple-repeated experiment or sample. The binomial distribution is a type of probability distribution with two possible outcomes (the prefix “bi” means “two” or “twice”). A coin flip, for example, has only two possible outcomes: heads or tails, and a test can have two possible outcomes.

A Binomial Distribution shows either (S)uccess or (F)ailure.

• The number of times the experiment runs is expressed by the first variable in the binomial formula, n.

• The likelihood of one particular outcome is represented by the second variable, p.

Consider the case where you wanted to know the chances of rolling a 1 on a die. The chance of rolling a one on any throw is 1/6 if you roll a die 20 times. If you roll 20 times, you’ll get a binomial distribution of (n=20, p=1/6). FAILURE would be “roll something else” and SUCCESS would be “roll a one.”  The binomial distribution would become (n=20, p=1/2) if the result was the likelihood of the die landing on an even number. This is due to the fact that tossing an even number has a half-probability.

Criteria

The following three conditions must also be met by binomial distributions.:

1. The number of observations or trials is fixed. To put it another way, you can only determine the likelihood of anything occurring if you do it a certain amount of times. This is self-evident: if you flip a coin once, you have a 50% chance of having tails. If you flip a coin 20 times, the chances of having tails are really close to 100 percent.
2. Each observation or trial is distinct from the others. To put it another way, none of the trials have any bearing on the likelihood of the next trial.
3. From one trial to the next, the likelihood of success (tails, heads, fail, or pass) is the same.

Binomial Distribution is a Discrete Distribution.

It defines the outcome of binary situations, such as a coin flip, where the outcome is either head or tails.

There are three parameters to it:

n stands for the number of trials.

p denotes the likelihood of each trial occurring (e.g. for toss of a coin 0.5 each).

Uniform Distribution

When any occurrence has an equal chance of occurring, this is referred to as likelihood.

For instance, random number generation.

There are three parameters to it:

a – lower bound – defaults to 0.0; b – upper bound – defaults to 1.0.

The Binomial Distribution | Probability and Statistics