Probability Rules

Rules

Complement

P (A^{'}) = 1 - P (A)

Addition rule

P (A \cup B) = P (A) + P (B) - P (A \cap B)

mutually exclusive: P(A ∩ B) = 0

Conditional probability

P (A ∣ B) = \frac{P (A \cap B)}{P (B)}

Multiplication rule

P (A \cap B) = P (A) \cdot P (B ∣ A)

independent: P(A ∩ B) = P(A)·P(B)

Bayes' theorem

P (A ∣ B) = \frac{P (B ∣ A) P (A)}{P (B ∣ A) P (A) + P (B ∣ A^{'}) P (A^{'})}

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