finite or countable set sample space countable probability
Modern definition:
The modern definition starts with a finite or countable set called the sample space, which relates to the set of all possible outcomes in classical sense, denoted by 



Ω


{\displaystyle \Omega }

. It is then assumed that for each element 



x
∈
Ω



{\displaystyle x\in \Omega \,}

, an intrinsic "probability" value 



f
(
x
)



{\displaystyle f(x)\,}

 is attached, which satisfies the following properties:
