Probability of an event

A probability of an event in a probability space $(\Omega,\mathcal{F},\mathbb{P})$ is the number $\mathbb{P}(A)$ assigned to an event $A\in\mathcal{F}$.

Because events are measurable sets and $\mathbb{P}$ is a probability measure , event probabilities satisfy the usual axioms (nonnegativity, countable additivity on disjoint events, and normalization).

Examples:

• In a fair coin toss space, the event $A=\{H\}$ has probability $\mathbb{P}(A)=1/2$.
• In the uniform space on $[0,1]$, the event $A=[0,1/2]$ has probability $\mathbb{P}(A)=1/2$.