A random variable follows a **Bernoulli distribution** if it only has two possible outcomes: 0 or 1.

For example, suppose we flip a coin one time. Let the probability that it lands on heads be *p*. This means the probability that it lands on tails is 1-*p*.

Thus, we could write:

In this case, random variable *X* follows a Bernoulli distribution.

In the real world there are many instances where random variables follow a Bernoulli distribution. Any scenario where a random variable can only take on one of two values follows a Bernoulli distribution.

There are two ways to simulate a Bernoulli distribution in R:

**Method 1: Use the dbinom() Function in Base R**

#calculate Bernoulli probabilities dbinom(c(0, 1), size = 1, p = 0.7)

This particular example will return the probability associated with an outcome of 0 and an outcome of 1 for a Bernoulli distribution that has a probability of success of p = 0.7.

Note that we use the **dbinom()** function to use the Binomial distribution function in R with a sample size of 1, which is simply the Bernoulli distribution.

**Related:** Bernoulli vs Binomial Distribution: What’s the Difference?

**Method 2: Use the dbern() Function from the Rlab package**

library(Rlab) #calculate Bernoulli probabilities dbern(c(0, 1), prob=0.7)

This particular example will return the probability associated with an outcome of 0 and an outcome of 1 for a Bernoulli distribution that has a probability of success of p = 0.7.

The following examples show how to use each of these methods in practice to simulate the Bernoulli distribution in R.

**Example 1: Use dbinom() to Simulate Bernoulli Distribution in R**

Suppose that we would like to calculate the probability associated with an outcome of 0 and an outcome of 1 for a Bernoulli distribution that has a probability of success of p = 0.7.

We can use the following syntax with the **dbinom()** function from base R to do so:

#calculate Bernoulli probabilities dbinom(c(0, 1), size = 1, p = 0.7) [1] 0.3 0.7

The output tells us:

- The probability of an outcome of 0 is
**0.3**. - The probability of an outcome of 1 is
**0.7**.

Note that the sum of these probabilities is 1, which is true of any Bernoulli distribution.

Feel free to change the value of p in the **dbinom()** function to simulate a Bernoulli distribution that has a different probability of success on a given trial.

**Example 2: Use dbern() to Simulate Bernoulli Distribution in R**

Suppose that we would like to calculate the probability associated with an outcome of 0 and an outcome of 1 for a Bernoulli distribution that has a probability of success of p = 0.2.

We can use the following syntax with the **dbern()** function from the **Rlab** package in R to do so:

library(Rlab) #calculate Bernoulli probabilities dbern(c(0, 1), prob=0.2) [1] 0.8 0.2

The output tells us:

- The probability of an outcome of 0 is
**0.8**. - The probability of an outcome of 1 is
**0.2**.

Once again, the sum of these probabilities is 1.

Feel free to use either the **dbinom()** function with a **size** argument of **1** or the **dbern()** function from the **Rlab** package in R to simulate a Bernoulli distribution.

**Additional Resources**

The following tutorials explain how to use other common statistical distributions in R:

How to Use the Chi-Square Distribution in R

How to Use the Multinomial Distribution in R

How to Use the Gamma Distribution in R

How to Plot an Exponential Distribution in R