Basic Probability Formulas

Probability Range

0 ≤ P(A) ≤ 1

Rule of Complementary Events

P(A^C) + P(A) = 1

Rule of Addition

P(A∪B) = P(A) + P(B) - P(A∩B)

Disjoint Events

Events A and B are disjoint iff

P(A∩B) = 0

Conditional Probability

P(A | B) = P(A∩B) / P(B)

Bayes Formula

P(A | B) = P(B | A) ⋅ P(A) / P(B)

Independent Events

Events A and B are independent iff

P(A∩B) = P(A) ⋅ P(B)

Cumulative Distribution Function

F_X(x) = P(X ≤ x)

Probability Mass Function

Probability Density Function

 

Covariance

Correlation

 

Bernoulli: 0-failure 1-success

Geometric: 0-failure 1-success

Hypergeometric: N objects with K success objects, n objects are taken.

 

See also