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Math — Conditional Probability

Multiplication, total probability and Bayes.

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

P(B) = \sum_i P(B \mid A_i)P(A_i)

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

\text{independent: } P(A \mid B) = P(A)