A discrete distribution describes the probability of occurrence of a random variable that can take on only a certain number of values. Common examples for this are the probabilities in a dice roll or getting a certain card in a deck of regular cards. In this guide, we’re going to show you how to calculate discrete probability in Excel.

## What is probability?

Probability is a branch of mathematics that shows how likely an event is to occur. In a nutshell, it is the ratio of the number of occurrences of an event to the total number of occurrences.

Let’s look at rolling a dice. A standard dice has 6 sides and each side has an equal chance to be on top. Thus, we can say each number has 1/6 = 0.1667 probability.

If you want to calculate the probability of getting 1 or 2 or 3 on a dice roll, you can sum up the probability values or use the **PROB** function.

## PROB function

The **PROB** function is a statistical function that can calculate the probability associated with a given range. The function allows you to set lower and upper limits to be able to calculate probability between.

x_range |
The range of numeric values which have associated probabilities. |

prob_range |
The range of probabilities associated with values in x_range. |

lower_limit |
The lower bound on the value for which you want to calculate the probability. |

[upper_limit] |
Optional. The lower bound on the value for which you want to calculate the probability.If this is omitted, the PROB function returns the probability for the x_range values equal to the lower_limit. |

## How to calculate discrete probability with PROB function

The first argument of the **PROB** function, **x_range**, accepts events by numerical values. Events, in this example, are the numbers of a dice. The second argument, **prob_range**, is for the probabilities of occurrences of the corresponding events. The rest of the arguments are for the lower and upper limits, respectively.

To return the probability of getting 1 or 2 or 3 on a dice roll, the data and formula should be like the following:

The formula returns *0.5,* which means you have a *50%* chance to get 1 or 2 or 3 from a single roll. Let’s check a more complex example for calculating discrete probability with 2 dices.

When you roll two dices, you can get numbers between 2 and 12. However, the probabilities of numbers are not equal this time. The table of numbers and probability values are below.

If your aim is to find the probability of a single event, you can use the **COUNTIF** function to count values above, based on the event value and divide it by the total number of events. You can find total number by multiplying dice numbers (6 * 6) or counting them using the **COUNT** function.

You can see that the most likely result is the number *7* with a probability of *0.1667*.