0 ≤ p(A) ≤ 1

p(S) = 1

Probability Formula

Addition Rule

If A B ≠ .

p(A B) = p(A) + p(B) − p(A B)

p(A B C) = p(A) + p(B) + p(C) − p(A B) − p(A C) − p(B C) + p(A B C)

Multiplication Rule

Independent Events

p(A B) = p(A) · p(B)

Dependent Events

p(A B) = p(A) · p(B|A)

Conditional Probability

Independent Events

p(A|B) = p(A)

Dependent Events

p(A|B) ≠ p(A)

Law of Total Probability

p(B) = p(A₁) · p(B|A₁) + p(A₂) · p(B|A₂ ) + ... + p(A_n) · p(B|A_n )

Bayes' Theorem

Expected Value

Variance of a Discrete Random Variable

Standard Deviation of a Discrete Random Variable

Binomial Distribution

Normal Approximation to the Binomial

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