Definition
Mutually exclusive events
Events with no shared outcome, so they cannot happen on the same trial.
What it means
The events do not overlap. Once one happens on a particular try, the other cannot happen on that same try.
Remember it
No overlap on one try.
Example
One card is chosen from cards numbered 1 to 5. Event A is “less than 3,” so A = {1, 2}. Event B is “greater than 4,” so B = {5}. The sets share no outcome, so the events are mutually exclusive.
Watch for
“Odd number” and “greater than 3” are not mutually exclusive for these cards because the outcome 5 belongs to both events.
Common mix-up
Mutually exclusive is not the same as independent; if one mutually exclusive event happens, the other is impossible on that trial.
Exact meaning
Events are mutually exclusive when their intersection is empty: they have no outcome in common and cannot both occur in the same trial.