# Category:Independent Events

This category contains results about **Independent Events**.

Definitions specific to this category can be found in Definitions/Independent Events.

Let $\EE$ be an experiment with probability space $\struct {\Omega, \Sigma, \Pr}$.

Let $A, B \in \Sigma$ be events of $\EE$ such that $\map \Pr A > 0$ and $\map \Pr B > 0$.

### Definition 1

The events $A$ and $B$ are defined as **independent (of each other)** if and only if the occurrence of one of them does not affect the probability of the occurrence of the other one.

Formally, $A$ is independent of $B$ if and only if:

- $\condprob A B = \map \Pr A$

where $\condprob A B$ denotes the conditional probability of $A$ given $B$.

### Definition 2

The events $A$ and $B$ are defined as **independent (of each other)** if and only if the occurrence of both of them together has the same probability as the product of the probabilities of each of them occurring on their own.

Formally, $A$ and $B$ are independent if and only if:

- $\map \Pr {A \cap B} = \map \Pr A \map \Pr B$

## Pages in category "Independent Events"

The following 7 pages are in this category, out of 7 total.