## What are Bernoulli Trials?

A

**Bernoulli trial**is an experiment with two possible outcomes: Success or Failure. “Success” in one of these trials means that you’re getting the result you’re measuring. For example:

- If you flip a coin 100 times to see how many heads you get, then the Success is
*getting heads*and a Failure is*getting tails*. - You might want to find out how many girls are born each day, so a girl birth is a Success and a boy birth is a Failure.
- You want to find the probability of rolling a double six in a dice game. A double six dice roll = Success and everything else = Failure.

Note that “Success” doesn’t have the traditional meaning of triumph or prosperity. In the context of Bernoulli trials, it’s merely a way of** counting the result you’re interested in**. For example, you might want to know how many students get the last question on a test wrong. As you’re measuring the number of incorrect answers, the “Success” is *answered incorrectly *and a “Failure” is answered *correctly*. Of course, this might get confusing so there’s nothing stopping you tweaking your hypothesis so that you’re measuring the number of correct answers instead of incorrect ones.

## Probability Distribution for Bernoulli Trials

**Bernoulli trials are a special case of i.i.d. trials;** Trials are i.i.d. if all the random variables in the trials have the same probability distribution.

The **probability distribution for a Bernoulli trial** is given by the binomial probability distribution:

Where:

- ! is a factorial,
- x is the number of successes,
- n is the number of trials.

## Assumptions for Bernoulli Trials

The three assumptions for Bernoulli trials are:

- Each trial has two possible outcomes: Success or Failure. We are interested in the number of Successes X (X = 0, 1, 2, 3,…).
- The probability of Success (and of Failure) is constant for each trial; a “Success” is denoted by the letter
*p*and “Failure” is*q*= 1 −*p*. - Each trial is independent; The outcome of previous trials has no influence on any subsequent trials.

## References

Governors State University. General PPT.

**CITE THIS AS:**

**Stephanie Glen**. "Bernoulli Trials: Definition, Examples" From

**StatisticsHowTo.com**: Elementary Statistics for the rest of us! https://www.statisticshowto.com/bernoulli-trials/

**Need help with a homework or test question? **With **Chegg Study**, you can get step-by-step solutions to your questions from an expert in the field. Your first 30 minutes with a Chegg tutor is free!

**Comments? Need to post a correction?** Please post a comment on our ** Facebook page**.