A stands for event. P stands for probability. An empty collection means that there are no events. Without events, the probability of natural events is zero. But if there is an event, the probability of the event can also be zero.

For example. A This collection is such an event {I am a woman}, and the probability of this event is 0, because I am a man. A is not empty at this time. There is an event in it, that is, "I am a woman."

Extended data

Let A and B be mutually incompatible events (AB=φ), then:

P(A∪B)=P(A)+P(B)

Inference 1: If A 1, A2, …, An are incompatible with each other, then: P (A1+A2+...+An) = P (A1)+P (A2)+…+P (An).

Inference 2: Let A 1, A2, ..., A form a complete event group, then: P (A1+A2+...+An) =1.

Inference 3:?

Contrary to event a.

Inference 4: if b contains a, then P (B-A) = P (B)-P (A).

Inference 5 (generalized addition formula):

For any two events a and b, there is P (A ∪ B) = P (A)+P (B)-P (AB).