Definition: Independent Events
Let \(B\) be an event with the probability \(0 < p(B) < 1\). We call the event \(A\) independent from \(B\), if the conditional probability of \(A\) given \(B\) and the conditional probability of \(A\) given the complement event \(\overline{B}\) are equal each other:
\[p(AB)=p(A\overline{B}).\]
Loosely speaking, the frequency of occurrence of \(A\) does not depend on whether \(B\) happened, or not.
Table of Contents
 Proposition: Characterization of Independent Events
 Proposition: Characterization of Independent Events II
 Definition: Mutually Independent Events
 Definition: Pairwise Independent Events
Mentioned in:
Proofs: 1
Thank you to the contributors under CC BYSA 4.0!
 Github:

References
Bibliography
 Bosch, Karl: "Elementare Einführung in die Wahrscheinlichkeitsrechnung", vieweg Studium, 1995, 6th Edition