The binomial distribution is a discrete probability distribution that represents the probabilities of binomial random variables in a binomial experiment. The binomial distribution is defined as a probability distribution related to a binomial experiment where the binomial random variable specifies how many successes or failures occurred within that sample space. It’s important for data scientists and professionals in other fields to understand this concept as binomials are used often in business applications.
The binomial distribution is a probability distribution that applies to binomial experiments. It’s the number of successes in a specific number of tries. The binomial distribution may be imagined as the probability distribution of a number of heads that appear on a coin flip in a specific experiment comprising of a fixed number of coin flips.
The requirements for a random experiment to be a Binomial experiment are as follows:
- A fixed number (n) of trials
- Each trial must be independent of the others
- Each trial must result in one of the two possible outcomes, called “success” (the outcome of interest) or “failure”.
- There is a constant probability (p) of success for each trial, the complement of which is the probability (1 – p) of failure, sometimes denoted as q = (1 – p)