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Concept

Mutually Exclusive Events

Two events

A

and

B

are said to be mutually exclusive or disjoint if the events cannot occur simultaneously. This means that

A

and

B

have no common outcomes, implying that the probability of

A

and

B

is zero.

$P (A and B) = 0$

By the Addition Rule of Probability, it can be concluded that the probability of $A$ or $B$ is equal to the sum of the individual probabilities.

$P (A or B) = P (A) + P (B)$

Below, some examples of mutually exclusive events are presented.

A given integer number is either even or odd.
The outcome of tossing a coin is either heads or tails.

One coin showing head and tail

Three or more events are mutually exclusive if all pairs are mutually exclusive.

In a soccer match, a team either wins, loses, or the result is a draw.
The outcome of rolling a dice is either $1,$ $2,$ $3,$ $4,$ $5,$ or $6 .$

Events can be mutually exclusive without being the only possible outcomes.

A given number is either negative or positive.
A card randomly drawn from a deck of cards is hearts or clubs.

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