Proposition: Characterization of Independent Events

Let \(B\) be an event with the probability \(0 < p(B) < 1\). Another event \(A\) is independent from \(B\), if any only if the probability of \(A\) equals the conditional probability of \(A\) given \(B\):

\[p(A)=p(A|B).\]

Loosely speaking, the frequency of occurrence of \(A\) does not change, if \(B\) also happened.

Proofs: 1

Proofs: 1


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References

Bibliography

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