What is the Difference Between Bernoulli and Binomial?

The main difference between Bernoulli and Binomial distributions lies in the number of trials and the outcomes they represent.

• Bernoulli Distribution: This distribution deals with the outcome of a single trial of an event, with two possible outcomes: 0 or 1. It is used when the outcome of an event is required for only one time. For example, if you toss a coin with a 25% probability of heads, a single toss of the coin has a Bernoulli distribution, with p = 0.25.
• Binomial Distribution: This distribution deals with the outcome of multiple trials of a single event, where each trial has two possible outcomes: 0 or 1. It is used when the outcome of an event is required multiple times. In order for a random variable to follow a Binomial distribution, the probability of "success" in each Bernoulli trial must be equal and independent. For example, if you toss a coin 3 times and record the number of heads, this is now a Binomial distribution with p = 0.5 (probability of success on a given trial) and n = 3 (number of trials).

In summary:

• Bernoulli distribution represents the outcome of a single trial with two possible outcomes.
• Binomial distribution represents the outcome of multiple trials with two possible outcomes, where the probability of success in each trial is equal and independent.

Comparative Table: Bernoulli vs Binomial

Here is a table comparing the differences between Bernoulli and Binomial distributions:

In summary, a Bernoulli distribution represents the outcome of a single trial with two possible outcomes, while a Binomial distribution represents the outcomes of multiple trials, each with the same probability of success, and multiple possible outcomes.