Difference

3. Probability: Relationship between Events

Difference

When two events $A$ and $B$ have overlapping outcomes, it might be interesting to analyze the event of $A$ NOT $B$ . This is also called the difference of $A$ and $B$ .
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Difference

Definition

The difference of events $A$ and $B$ are all outcomes that are classified as $A$ , but NOT as $B$ .

The difference of $A$ and $B$ is denoted as $A\,\backslash \,B$ .

Note that $A\, \backslash \,B$ is not the same as $B\,\backslash \, A$ .

Consider the events $A$ and $B$ where:

$A = \{1, 2, 3, 4\}$
$B = \{2, 4, 6, 8\}$

Then the difference of $A$ and $B$ ( $A$ NOT $B$ ) is defined as:
$A\, \backslash \,B = \{1, 3\}$

And the difference of $B$ and $A$ ( $B$ NOT $A$ ) is defined as:
$B\, \backslash \,A = \{6, 8\}$