# How do overlapping events differ from mutually exclusive events?

Nov 11, 2017

See explanation.

#### Explanation:

Two events are mutually exclusive if they cannot occur at the same time (i.e. their intersection is the empty set).

If the intersection of 2 events is not empty, they are overlapping.

Example 1:

$A$ - a prime number is thrown on a single die.

$B$ - an even number is thrown on a single die.

These two events are overlapping because number $2$ is both prime and even, so

$A \cap B = \left\{2\right\}$

Example 2:

$A$ - an even number is thrown on a die

$B$ - an odd number is thrown on a die

These two events are mutually exclusive because there are no numbers which are odd and even at the same time, so

$A \cap B = \emptyset$