# Probability Distribution- Binomial

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Probability Distribution- Binomial: The Binomial probability distribution summarizes the likelihood that a value will take one of the two possible independent values. The Binomial distribution has following assumptions:

1. Each trial can take one of the two possible outcomes
2. Each trial has equal probability of success or failure
3. Each trial is mutually exclusive and independent of each other

The Binomial distribution helps to determine specified number of success in a given number of trials.

In Binomial Distribution, each experiment is said to be random with two possible outcomes while one trail does not have effect on any other trial. In other words, Binomial distribution is a series of multiple, independent and identically distributed trials. Each trial of Binomial distribution is also known as Bernoulli trial.

Bernoulli distribution: Bernoulli distribution is a special case in Binomial distribution when number of trail is equal to one.

Binomial distribution can be described by the following formula:

Where:

n = Total number of trials

x = total number of successes

p = probability of success

q = probability of failure