Mathematics · Cheatsheet

Probability & Distributions

Chapter 1 · Probability

📋 Reference · always available

Basic probability

P(A) = \frac{\text{favourable}}{\text{total}}

Complement

P(A') = 1 - P(A)

Union

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

Conditional

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

Independence

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

Combining events

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

Conditional / independent

P(A|B)=\tfrac{P(A\cap B)}{P(B)};\;\text{indep}: P(A\cap B)=P(A)P(B)

Complement & tree

P(\text{at least one})=1-P(\text{none})

Multiply along branches; add across outcomes.

Common trap

Mutually exclusive (can’t both happen) ≠ independent (one doesn’t affect the other).