That is, the probability of these two events adds up to 1, that is, these two events cover all situations, either this event occurs or another event occurs.

Mutually exclusive events,

These two events, if one event happens, the other event will not happen. Of course, it is also possible that neither event will happen. (But one of the opposing events is bound to happen. )

Generally speaking, the opposing event must be mutually exclusive events, but mutually exclusive events is not necessarily an opposing event. That is, the opposite event is a stronger conclusion.

Example: roll the dice,

Event 1: The number of points is singular; Event 2: the number of points is even; Event 3: The number of points is 1 or 2; Event 4: The number of points is 5

Then event 1 and event 2 are opposite events.

Events 3 and 4 are mutually exclusive events.

For the theme you added, you chose C. . .

"Just one black ball" and "Just two black balls" are mutually exclusive.

You see, "there happens to be a black ball" is {"a black ball and a red ball"}.

"There are exactly two black balls" is {"two black balls"}

The things in the two sets are different, so they are mutually exclusive, but the two sets cannot contain all the situations.

Because there is no situation where both are red balls, this is not an opposing event.