What is Binomial Distribution |

**Binomial probability distribution**

The binomial distribution is a discrete probability distribution used in probability theory and statistics that only offers two possible outcomes for an experiment: success or failure. For instance, there are just two possible outcomes when tossing a coin: heads or tails. Similarly, there are only two possible outcomes while taking a test: pass or fail.

when X denotes the number of success in 'n' trials of a binomial probability experiment it is called a binomial random variable and its probability distribution is called binomial probability distribution.

### Binomial Distribution Formula

*P (x) = ( X^n) p^x q^(n-x)*

(where *X *= 0,1,2,3....n)

*p * = probability of success

*q * = probability of failure

*x *= number of success

*n-x* = number of failures

Note : The binomial probability distribution has two parameters N and P.

### Properties of Binomial Distribution

The following are the properties of the binomial distribution:- Two things could happen: truthful or untrue, successful or unsuccessful, yes or no.
- For every trial, the chance of success or failure stays constant.
- Since each experiment is conducted independently of the others, the results of one trial do not influence the results of subsequent trials.
- Trials can be repeated a fixed number of times (n times) or in an independent manner (n).
- Out of n separate trials, only the success rate is computed.

**Binomial Experiment**

Many experiments consist of repeated independent trials. Each trial having only two possible outcomes. For example: The two possible outcomes of a trial maybe head and tail, success and failure, good and defective.

If the probability of each outcome remain the same throughout the trials, then such trials are called bernoulli trial and the experiment having 'n' Bernoulli trial is called binomial experiment.

**Properties of Binomial Experiment**

1. The outcome of each trial may be classified into one of two categories success and failure.

2. The probability of success denoted by 'p' remains constant for all trials.

3. The successive trials are all independent.

4. The experiment is repeated a fix number of times.