3. Probability: Relationship between Events
Mutual Exclusivity
In some cases, two events will have overlapping outcomes.
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The event of rolling a die and getting an even number #\{2, 4, 6\}# has overlapping outcomes with the event of rolling a die and getting a number greater than 2 #\{3, 4, 5, 6\}#; namely the outcomes #4# and #6#.
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Other events do not overlap at all. Such events are said to be mutually exclusive.
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The event of rolling an odd number #\{1, 3, 5\}# and the event of rolling an even number #\{2, 4, 6\}# have no overlapping outcomes at all.
Mutual exclusivity
Definition
Two events #A# and #B# are mutually exclusive or disjoint when they have no outcomes in common.
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Note that any event #A# and its complement #A^c# are, by definition, mutually exclusive.
