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Probability Theorems

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Addition Rule for Non-Mutually Exclusive Events

P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)

Independent Events

P(A \text{ and } B) = P(A) \times P(B)

Expected Value

E(X) = \sum_{i=1}^n x_iP(x_i)

Conditional Probability

P(A|B) = \frac{P(A \text{ and } B)}{P(B)}

Addition Rule for Mutually Exclusive Events

P(A \text{ or } B) = P(A) + P(B)

Law of Total Probability

P(A) = \sum_{i=1}^n P(A|B_i)P(B_i)

Bayes' Theorem

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

Multiplication Rule

P(A \text{ and } B) = P(A)P(B|A) = P(B)P(A|B)

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