What is a Bernoulli Trial?
A Bernoulli trial is one of the simplest experiments you can conduct in probability and statistics. It refers to an experiment where you can have one of two possible outcomes, like “Yes” and “No” or “Heads” and “Tails.” Examples include:
- Coin tosses: You want to record how many coins landed heads up and how many landed tails up.
- Births: You want to find out how many boys are born and how many girls are born each day.
- Rolling Dice: You want to find out the probability of a roll of two die resulting in a double six.
Bernoulli trials are usually phrased in terms of success and failure. Success doesn’t mean success in the usual way — it just refers to a specific outcome you want to record. For example, you might want to find out how many boys are born each day, so you call a boy birth a “success” and a girl birth a “failure.”
A double six die roll would be your “success” and everything else rolled would be considered a “failure.”
What is a Bernoulli Trial: Independence
An important part of every Bernoulli trial is that each action must be independent so that the probabilities remain consistent. In other words, each event must be completely separate and have nothing to do with the previous event. For example, lotto numbers generally come out of a ball (the numbers aren’t replaced) so the probability of successive numbers being picked depends upon how many balls are left; when there’s a hundred balls, the probability is 1/100 that any number will be picked, but when there are only ten balls left, the probability shoots up to 1/10. While it’s possible to calculate those probabilities, it isn’t a Bernoulli trial because the events (picking the numbers) are connected to each other.
The Bernouilli process leads to several probability distributions: the binomial distribution, geometric distribution, and negative binomial distribution.