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\}#
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