Binomial Probability Distribution Tutorial


In statistics , the binomial distribution is a discrete probability distribution that indicates the number of successes when performing a sequence of n independent trials with each other, with a fixed probability (p) of success occurring between those trials.

The binomial distribution is one of the theoretical probability distribution models that is used when the discrete random variable is the number of successes in a sample composed of n observations. It is one of the most useful probability distributions used in quality control, production, research, etc.

Binomial Distribution in Data Science:


The Binomial Distribution is related to the Bernoulli distribution which is a random variable distribution X that takes only values ​​of zero and one (success and failure), when a single experiment is performed.

The binomial distribution is applied when a "n" number of times the Bernoulli experiment is performed, each trial being independent of the previous one. The variable can take values ​​between 0 (if all experiments have been failure) and n (if all experiments have been successes). A discrete variable is one that can only take a finite number of values ​​between any two values ​​of a characteristic.

Binomial Probability Distribution Formula:


The probability function of the binomial distribution, also called the Bernoulli distribution function , is expressed with the formula:




The binomial distribution is a distribution of probabilities that arises when the following conditions are met:

  • The number of trials or repetitions of the experiment (n) is constant.
  • In each trial there are only two possible outcomes (success or failure, defective or noi defective).
  • The probability of each possible outcome in any trial remains constant.
  • In each trial, the two possible outcomes are mutually exclusive.

Binomial Probability Distribution Example:




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