### Chapter 3. Probability: Relationships 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\}#

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