Binomial experiment is described as a statistical experiment that contains fixed number of trials and can have either of the two outcomes - true or false. More specifically, a binomial experiment must satisfy the following properties -

- Binomial experiment is consisting of a fixed number of actions which are termed as
**trials**. We can say that number of trials are fixed in such experiment. - Each trial must be independent of one another. This means that the success or failure of one trial must not affect another trial.
- There can be one of the exactly two possible outcomes in each trial, such as - success or failure, pass or fail.
- The probability of each outcome is same in each trial. Therefore, for a trial, the probability of success is same as that of failure.
- The sum of probability of success and failure is "1". So, if the probability of success in a trial is "
**p**", then the probability of failure in that trial is "**1 - p**".

Binomial Random Variable

Total number of successes in a binomial experiment is known as binomial random variable. If "

According to the formula for binomial experiment, the probability of k successes in total n trials can be calculated as -

$P(k) =\ ^{n}\textrm{C}_{k}\ p^{k}\ (1-p)^{n-k}$

Where,P(k) = Probability of k successes.

p = Probability of success in each trial.

1 - p = q = Probability of failure in each trial.

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