What's the difference between mutually exclusive events and opposing events?

The connection between the two is that the opposing events belong to a special kind of mutually exclusive events. You can see the difference between the two by definition. The union of an event itself and its opposite events is equal to the total sample space; But if two events are mutually exclusive events, it means that one event will not happen, but it does not emphasize that their union is the whole sample space.

For example: suppose the whole work is about the weather, then event A= sunny day; Event B= rain, obviously it can't happen when A happens, so the two are mutually exclusive. But they are not antagonistic, because there are other possible weather besides sunny and rainy days, such as snow and hail, so the union of sunny and rainy days does not include all possible situations (the whole sample space), so they are not antagonistic events.

Mutually exclusive events:

The intersection of events A and B is empty, and A and B are mutually exclusive events, also called incompatible events.

Mutex: For event A, B, A crosses B= empty set. That is, a and b can't happen at the same time.

Mutually exclusive events only asked that two events should not happen at the same time.

Opposing events:

One of them must happen. These two mutually exclusive events are called antagonistic events.

Opposition: a special case of mutual exclusion. In the case of mutual exclusion, it is also necessary to satisfy that A and B are complete sets. That is, A and B only appear once and must appear once.

The opposite event is that if one of the two events does not occur, the other event must occur, that is, the two times are mutually exclusive and form a complete set.