Definition: Mutually Independent Events

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:

\[p(A_I)=\prod_{i\in I}p(A_i).\]

  1. Proposition: Replacing Mutually Independent Events by Their Complements

Definitions: 1
Proofs: 2 3 4
Propositions: 5 6

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  1. Bosch, Karl: "Elementare Einf├╝hrung in die Wahrscheinlichkeitsrechnung", vieweg Studium, 1995, 6th Edition