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Bayes' theorem of probability

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Derivation of the Bayes' theorem can be made by the multiplication rule of probability and some algebra.

P(A \cap B) = P(A) \cdot P(B \mid A))


P(A \cap B) = P(B) \cdot P(A \mid B))

Subtracting these two equations leads:

0 = P(B) \cdot P(A \mid B)) - P(A) \cdot P(B \mid A))

and some algebraic transformation

P(A) \cdot P(B \mid A)) = P(B) \cdot P(A \mid B))

yields the theorem

P(B \mid A)) = \frac{P(B) \cdot P(A \mid B))}{P(A)}

Tags: Statistics

Categories: Mathematics


(c) Mato Nagel, Weißwasser 2004-2013, Disclaimer