(6) If , event and event are said to be mutually incompatible , or mutually exclusive . The meaning is: event and event cannot occur at the same time.
For example , basic events are pairwise mutually exclusive.
(7) If and , then event and event are said to be opposite events , or event and event are said to be inverse events . The meaning is: for each trial, one and only one of events and occurs. The opposite event of event is denoted as . then,
.
Note: In high school, we initially learned the concepts of mutually exclusive events and opposing events .
Two mutually opposing events must be mutually exclusive events; conversely, mutually exclusive events are not necessarily opposing events. Moreover, the concept of mutual exclusion applies to multiple events, but the concept of opposition only applies to two events.
(8) Complete event group
Assume is a finite or countable event. If it satisfies
① , , ,
② ,
then is said to be a complete event group , also known as
is a division of sample space .
Obviously, and form a complete event group.