### 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.:

**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.**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.****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