# Mutually exclusive events

Two events are mutually exclusive if they cannot both happen at once. Their overlap is zero, so P(A or B) is just P(A) + P(B). This is different from being independent.

Statistics (university) · Part 02: Probability · Card 3 of 8 · Last updated 2026-10-19

## Analogy

You cannot be in Paris and Tokyo at the same moment. Those two events exclude each other.

## Example

**One card, two events**

P(heart) = 13/52 = 1/4
P(spade) = 13/52 = 1/4
P(heart and spade) = 0
P(heart or spade) = 1/4 + 1/4 = 1/2

## In practice

Drawing one card, being a heart and being a spade are exclusive. The probability of both is 0.

## Practice

### Flashcards

- **Can mutually exclusive events with positive probability be independent?** No. If one happens the other cannot, so they affect each other.

## Questions people ask

### Are mutually exclusive events independent?

No, usually the opposite. If A happens, B cannot, so knowing A changes the chance of B to zero. Independent events do not affect each other at all. Exclusive events with positive probabilities are therefore always dependent, which is why the two ideas should never be confused when you set up a calculation.

### How can I tell if two events are mutually exclusive?

Ask whether both can happen in the same trial. Rolling a 2 and rolling an odd number on one die cannot both occur, so they are exclusive. Rolling a 2 and rolling an even number can both occur, so they are not.

## Related concepts

- [Independent events](https://studyvisually.com/learn/science/statistics-university/statistics-university-part-2/statistics-university-part-2-concept-4)
- [Addition rule](https://studyvisually.com/learn/science/statistics-university/statistics-university-part-2/statistics-university-part-2-concept-2)

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