Chapter 13 – Probability

Key Formulas

Quick Reference

Probability Basics

P(E) = n(E)/n(S)
0 ≤ P(E) ≤ 1
P(S) = 1, P(∅) = 0

Addition Rule

P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
For disjoint events: P(A ∪ B) = P(A) + P(B)

Conditional Probability

P(A|B) = P(A ∩ B) / P(B), P(B) > 0
P(A ∩ B) = P(A)P(B|A)

Independent Events

A and B independent if P(A ∩ B) = P(A)P(B)
Then P(A|B) = P(A), P(B|A) = P(B)

Bayes' Theorem

P(Ai|B) = P(B|Ai)P(Ai) / Σj P(B|Aj)P(Aj)

Total Probability

P(B) = Σi P(B|Ai)P(Ai)
for mutually exclusive exhaustive Ai