# Mutually exclusive events

Events that cannot happen at the same time. For these, you add their probabilities, and the probabilities of all outcomes add to 1.

Maths (school) · Part 08: Probability and statistics · Card 3 of 8 · Last updated 2026-10-19

## Analogy

Like a traffic light: it cannot be red and green at once.

## Example

**Bag: 5 red, 3 blue, 2 green**

P(red or blue) = 5/10 + 3/10 = 8/10
P(not green) = 1 - 2/10 = 8/10

## In practice

If the chance of rain is 0.3, the chance of no rain is 0.7.

## Practice

### Flashcards

- **If P(rain) = 0.3, what is P(no rain)?** 0.7, since probabilities add to 1.

## Questions people ask

### What does P(not A) equal?

It equals 1 - P(A). Either the event happens or it does not, so the two probabilities add to 1. If P(rain) is 0.3, then P(no rain) is 1 - 0.3 = 0.7. It is often the quickest route. It is useful whenever counting the chances of the event not happening is easier than counting it happening.

### When do you add probabilities?

Add when you want the chance of one event OR another and they cannot both happen. For one dice roll, P(1 or 2) = 1/6 + 1/6 = 2/6. If the events can overlap, adding gives too much. For overlapping events, subtract the overlap once, or you will count those outcomes twice.

## Related concepts

- [Probability scale](https://studyvisually.com/learn/science/maths-school/maths-school-part-8/maths-school-part-8-concept-1)
- [Relative frequency](https://studyvisually.com/learn/science/maths-school/maths-school-part-8/maths-school-part-8-concept-2)
- [Independent events](https://studyvisually.com/learn/science/maths-school/maths-school-part-8/maths-school-part-8-concept-4)
- [Tree diagrams](https://studyvisually.com/learn/science/maths-school/maths-school-part-8/maths-school-part-8-concept-5)

Web page: https://studyvisually.com/learn/science/maths-school/maths-school-part-8/maths-school-part-8-concept-3
Study this card in the app: https://studyvisually.com/app/learn?category=maths-school&card=maths-school-part-8-concept-3