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

Lesson Slides

The slider below shows another real example of mutually exhaustive events. Open the slider in a new tab

A Note on Notation

The probability of an event can be written as:
P(Event)
A letter or symbol can be used to represent an event. For example, let H be the event that a coin lands on Heads 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.
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See Also

What is probability?