# Sum of probabilities – What is it, definition and concept

The sum of probabilities or addiction rule establishes the way to add two or more probabilities depending on whether or not the events are mutually exclusive.

The sum of probabilities is a widely used tool in the field of statistics. It allows knowing the probability that different events occur.

In this way, we can know how to add probabilities, since it is not as simple as doing it with numbers. As we will see, it depends on whether the events can occur at the same time or not. In addition, we have to mention the multiplication rule.

In the calculation of probabilities there are two essential rules, the addictive and the multiplicative. The first is used to add the probability of two or more events. It is the one that we will see and it will depend on whether or not they are mutually exclusive, that is, if they can occur at the same time.

The multiplication rule is closely related to the addition rule. We will only mention that this depends on whether or not two events are independent. In this way, if they are not independent, an intersection between them can occur with a probability that is calculated with this rule.

## Types of events in the sum of probabilities

When we add probabilities we can find two cases. One is that the events can occur at the same time. The other is that if one occurs, the other cannot occur. This will affect how the sum of probabilities is performed. Let’s look at both situations.

### nonexclusive events

This is the most common case. In it, in addition to occurring separately, they have a probability of occurring at the same time, that is, they are not mutually exclusive. In this case, the sum of probabilities is calculated as the sum of each separate event subtracting the probability of both at the same time.

### Mutually exclusive events

This is the simplest case. In it the probability of occurrence of two events at the same time is zero (A intersection B). This means that both cannot occur at the same time. Therefore, its form of calculation is the sum of the probability of one and the other.

## Example of sum of probabilities

Let’s see, finally, an example of sum of probabilities. In this case, with a dice. We will calculate the probability of getting a 4 or a 6. Let’s note that they cannot occur at the same time, something that would happen in others such as the probability of being blond and speaking English.

We can see that, in this case, the sum of probabilities is simply that of both happening separately. It is obvious that they cannot occur at the same time, we can never get a 4 and a 6 in the same roll with a single die.