What Are Mutually Exclusive Events?

What Are Mutually Exclusive Events?

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

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The slider below shows another real example of mutually exhaustive events.

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See Also

What is probability?