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:

\[p(A|B)=p(A|\overline{B}).\]

Loosely speaking, the frequency of occurrence of \(A\) does not depend on whether \(B\) happened, or not.

  1. Proposition: Characterization of Independent Events
  2. Proposition: Characterization of Independent Events II
  3. Definition: Mutually Independent Events
  4. Definition: Pairwise Independent Events

Proofs: 1


Thank you to the contributors under CC BY-SA 4.0!

Github:
bookofproofs


References

Bibliography

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