## Quick Reference

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, *A*_{1}, *A*_{2},…, *A** _{n}*,

P(*A*_{1} ∩ *A*_{2} ∩…∩ *A** _{n}*)=P(

*A*

_{1})×P(

*A*

_{2})×…×P(

*A*

*).*

_{n}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.

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