If P (A) ≥ 0, P (B ∨ A) can be defined. Generally, the occurrence of A has an impact on the probability of B, so conditional probability P (B ∨ A) ≠ P (B), and only when the occurrence of A has no effect on the probability of the occurrence of B (that is, A and B are mutually independent) can there be a conditional probability P (B ∨ A)=P (B). At this time Multiplication theorem P(A∩B)=P(B∣A)P(A)=P(A)P(B). therefore
Definition: Let A and B be two events. If the equation P (A ∨ B)=P (AB)=P (A) P (B) is satisfied, then events A and B are said to be independent of each other
Note: 1. P (A ∨ B) is P (AB)
2. If P (A) ＞ 0, P (B) ＞ 0, then A and B are mutually independent from A and B Incompatibility It cannot be established at the same time, that is, independence must be compatible and mutual exclusion must be linked Easy to popularize: Let A, B and C be three events. If P (AB)=P (A) P (B), P (BC)=P (B) P (C), P (AC)=P (A) P (C), P (ABC)=P (A) P (B) P (C), then events A, B and C are said to be mutually independent
More generally, A1, A2,.., An are n (n ≥ 2) events Product event The probability of is equal to the product of the probabilities of each event, which means that events A1, A2,..., An are mutually independent 
