Mutually Exclusive Events

If two events are mutually exclusive only one or the other of the two can occur and the probability of either occurring is additive:

$P\left ( A\cup B \right )=P\left ( A \right )+P\left ( B \right )$

Multiple events E1, E2, ..., En are said to be mutually exclusive if the occurrence of any one of them implies the non-occurrence of the remaining n − 1 events.

An Example

A good example of the probability of mutually exclusive events is calculating the probability of drawing a King or Queen from a deck of cards. There are 4 Kings in the deck, so the probability of drawing a King is 4/52, or 1/13. And since there are also 4 Queens in the deck, the probability of drawing a Queen is also 1/13. So, if:

$A=\left ( drawing\, a\, King \right ), \: B=\left ( drawing\, a\, Queen \right )$

then the probability of drawing a King or Queen is:

$P\left ( A\cup B \right )=P\left ( A \right )+P\left ( B \right )=\frac{1}{13}+\frac{1}{13}=\frac{2}{13}=.153846...$

Mutually Exclusive Events

An Example

References