math-probability-conditional-probabilities.html
* created: 2025-10-28T16:45
* modified: 2025-10-29T19:37
title
Conditional Probalities
description
Something happening on the basis that something else happend before.
Conditional Probabilities
Conditional probability: The outcome B has the prerequisite that A happened before; this is written as:
Pr(B|A)
If Pr(A) \neq 0. The conditional probability that B happens under the condition of A is defined through:
Pr(B|A) = \frac{Pr(A \cap B)}{Pr(B)}
Useful properties
Multiplication:
Pr(A \cap B) =Pr(A|B) \cdot Pr(B)
Bayes' theorem: With A and B being outcomes with Pr(A) \neq 0 and Pr(B) \neq 0, the following holds:
Pr(A|B) = \frac{Pr(A)}{Pr(B)} \cdot Pr(B|A)