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# Mutually Exclusive Events

(KS3, Year 7)

## The Lesson

Two or more events are mutually exclusive if they cannot happen at the same time.## A Real Example of Mutually Exclusive Events

It is easier to understand mutually exclusive events with an example.## Tossing a Coin

A tossed coin can either land as**Heads**or as

**Tails**. It cannot land as both at the same time.

**Heads**and

**Tails**are mutually exclusive events.

## Exhaustive Events

A set of events are*exhaustive*if they include all possible outcomes.

**Heads**and

**Tails**are exhaustive events because they are all the possible outcomes of tossing a coin.

## Probabilities of Exhaustive Events Sum to 1

If a set of mutually exlusive events are exhaustive, their probabilities add up to 1. If a coin is tossed, it must land as either**Heads**or

**Tails**. That is a certainty.

*P(Heads) + P(Tails) = 1*

## A Note on Notation

The probability of an event can be written as:*P(Event)*

**H**be the event that a coin lands on

**H**eads when it has been tossed. We can denote the probability of getting heads as:

*P(H)*

## Many Events Are Not Mutually Exclusive

Many events are not mutually exclusive. It is possible to be male and have brown hair. It is possible for it to be a Monday and for it to be raining outside.**Help Us To Improve Mathematics Monster**

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