What is an independent event? It is an event that does not affect each other, that is, whether event A happens or not has nothing to do with event B. However, one of the incompatible events happens, and the other definitely cannot happen, which is mutually influential. So the independence event must not be mutually exclusive events.

2. Incompatible events are not necessarily antagonistic events, but antagonistic events are mutually incompatible events.

Incompatible events include opposite events. Incompatible events have also been mentioned above, that is, at most one of several events occurs. If one of them occurs, then the rest will definitely not happen. The opposite event is an incompatible event that only contains two events, A and B. If A happens, B will not happen. If b happens, a will never happen.

3. Any two events contained in incompatible events will not intersect.

This is determined by the definition of mutually incompatible events, that is, events that cannot occur at the same time.

For example, the World Cup includes Holland, England and the United States. If the Netherlands wins the championship, then England and the United States must not win the championship. If England wins the championship, the Netherlands and the United States must not win it. In this example, the Dutch team won the championship, the British team won the championship, and the American team won the championship. This is an incompatible event.

4, such as 2, incompatible events are not necessarily antagonistic events. I don't understand why you said that incompatible events must not be antagonistic events.

This is an independent event. Because the two will not affect each other.

PA∪B stands for the first front and the second front. In independent activities, ABC, PABC = PA∠B∠c B ∠ C.

When neither A nor B occurs or at least one probability of A and B is 0, the independent event PAB is 0. Other conditions are not 0.