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Mutually Exclusive Events

(KS3, Year 7)

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.

heads or tails

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.

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.