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Binomial Experiment

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".
For Example : Toss of a coin with fixed trials is a binomial experiment in which possible outcome is either head or tail.

Binomial Random Variable

Total number of successes in a binomial experiment is known as binomial random variable. If "n" number of trials were performed in a binomial experiment and there are "k" number of successes out of n trials, then "k" will be termed as binomial random variable.

Formula for Binomial Experiment
According to the formula for binomial experiment, the probability of k successes in total n trials can be calculated as -
$P(k) =\ ^{n}\textrm{C}_{k}\ p^{k}\ (1-p)^{n-k}$
P(k) = Probability of k successes.
p = Probability of success in each trial.
1 - p = q = Probability of failure in each trial.

Related Calculators
Binomial Experiment Calculator Binomial Calculator
Binomial Confidence Interval Calculator Binomial Multiplication Calculator

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