Proposition: Characterization of Independent Events II

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 the joint event \(A\cap B\) equals the product of the probabilities of \(A\) and \(B\):

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

If in addition, \(0 < p(A) < 1\), then \(B\) is independent from \(A\).

Proofs: 1

Definitions: 1 2


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References

Bibliography

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