# Mutually exclusive events

We cannot flip head and tail on the same flip. **Either we flip head or tail. These two events are mutually exclusive, as one excludes the other**. They cannot happen at the same time.

## Mutually exclusive events examples

If you draw **ace of spades in the first draw without replacement**, there are no ace of spades to draw in the second draw. One event cannot take place, if the other has occurred. Therefore they are mutually exclusive and also dependent events. If one occurs, the other cannot occur.

If we were to pick an integer between 11 and 20, what would **the probability be that we choose a number that is both even and odd? **None! It would not be possible to choose a number that is even and odd at the same time. They are mutually exclusive events.

## Mutually exclusive events in a Venn diagram

A Venn diagram for mutually exclusive events shows that there is no common space between A and B. No joint section, no intersection:

Thus, the **addition rule** **or addition principle**:

** **

## Calculation of choosing either even or odd

Say that we again are to **choose a number between 11 and 20**. Let A be the event that you choose an even number. Let B be the event that you choose an odd number:

You have the probability of choosing **even or odd** numbers. **One plus the other**. A+B, which is expressed:

The probability of choosing either an even or an odd number is 1 = 100%.

## Mutually exclusive events vs independent events

We recall this comparing between mutually exclusive and independent events:

As illustrated in the figure above, independent events can happen at the same time and do not affect the outcome of one another, whereas mutually exclusive they do affect the outcome of one another and cannot occur at the same time.

## Learnings resources

- Jbstatistics’ video: Are mutually exclusive events independent?

#### Carsten Grube

Freelance Data Analyst

##### Normal distribution

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