I find that sometimes in probability (geared towards non-math majors), the definition of the sample space will involve things such as:
"a set of possible outcomes of a random experiment".
I guess here "possible outcomes" and "random experiment" are not rigorous definitions.
A similar one can be found on Wikipedia: (https://en.wikipedia.org/wiki/Sample_space)
"the sample space of an experiment or random trial is the set of all possible outcomes or results of that experiment."
It just seems a bit odd to me that probability theory rests upon a common-place/colloquial understanding of what a "random experiment" is.
Can this "sample space" and in particular "random experiment/trial" definition be more precise (or is this a Principia Mathematica type of scenario, i.e. not worth defining it rigorously)?