By extending the characterization of independent events from two to \(n\) events \(A_1,...,A_n\), we call them mutually independent, if for any subset of indices \(I\subset \{1,\ldots,n\}\), the probability of joint event. \[A_I:=\bigcap_{i\in I} A_i\] equals the product of all individual probabilities:
\[p(A_I)=\prod_{i\in I}p(A_i).\]
Definitions: 1
Proofs: 2 3 4
Propositions: 5 6