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# Binomial Distribution

## What is Binomial Distribution?

The binomial distribution is a probability distribution that summarises the likelihood that, under a given set of parameters or assumptions, a value takes one of two independent values.

Binomial distribution's underlying assumptions are that for each trial, there is only one outcome, that each test has the same probability of success, and that each trial is mutually exclusive or independent of each other.

Binomial distribution, as opposed to continuous delivery, such as normal distribution, is a standard discrete distribution used in statistics.

## Understanding Binomial Distribution

Binomial distribution summarises the number of trials or observations when each trial has the same likelihood of a particular value being achieved. The binomial distribution determines the probability of a given amount of successful outcomes being observed in a specified number of trials.

A binomial distribution's expected value, or mean, is calculated by multiplying the number of trials by the probability of success. For example, in 100 trials, the expected number of heads is 50, or (100 * 0.5).

Another typical example of a binomial distribution is the estimation of chances of success in basketball for a free-throw shooter where 1 = a basket is made and 0 = a miss.

## Binomial Distribution Example

The binomial distribution is calculated by multiplying the likelihood of success raised to the power of the number of successes and the possibility of failure raised to the power of difference between the number of successes and number of tests. Multiply the product, then, by combining the number of trials with the number of successes.

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