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Two events are said to be independent if knowing that one has occurred has no effect on the probability of the other event happening, i.e., P(A|B) = P(A).

Note: P(B|A)= P(B Ç A)/P(A)= P(A|B)P(B)/P(A)= P(A)P(B)/P(A) = P(B)

Thus the independence is "symmetric."
 
 

Also as a corollary, if A and B are independent, then

P(A Ç B) = P(A|B)P(B) = P(B|A)P(A) = P(A)P(B)

In fact we say that A and B are independent if, and only if P(A Ç B) = P(A)P(B).

In general, events E₁, E₂, ..., E_n are said to be mutually independent if the probability of the intersection of any number of these events (2 or 3 or 4 or...or n) is equal to the product of the individual probabilities of each event.