Law for probabilities stating that if A and B are independent events then
P(A ∩ B)=P(A)×P(B),
and, in the case of n independent events, A1, A2,…, An,
P(A1 ∩ A2 ∩…∩ An)=P(A1)×P(A2)×…×P(An).
This is a special case of the more general law of compound probability, which holds for events that may not be independent. In the case of two events, A and B, this law states that
P(A ∩ B)=P(A)×P(B|A)=P(B)×P(A|B).
For three events, A, B, and C, this becomes
P(A ∩ B ∩ C)=P(A)×P(B|A)×P(C|A ∩ B).
There are six (=3!) alternative right-hand sides, for example P(C)×P(A|C)×P(B|C ∩ A). The generalization to more than three events can be inferred. For definitions of symbols, see conditional probability; intersection.
Subjects: Probability and Statistics.