P(AB)=P(A)P(B)

Then A and B are independent events, that is, the occurrence of B has no effect on the probability of A, and the occurrence of A has no effect on the probability of B;

Suppose three events, a, b and c, if any:

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)

It is said that they are independent of each other; If only the first three equations are satisfied, it is independent in pairs.

Paired independence does not guarantee mutual independence;

Let ω = {w 1, w2, w3, w4}, p ({wi}) = 1/4 (I = 1, 2,3,4), a = {w 1, w2}.

Because AB=AB=BC={w 1}, there is.

P(AB)=P(A)P(B)

P(BC)=P(B)P(C)

P(AC)=P(A)P(C)

Therefore, A, B and C are independent of each other, but they are not independent of each other because:

P(ABC)= P({ w 1 })= 1/4≦( 1/2)*( 1/2)*( 1/2)= P(A)P(B)P(C)