studying myself and trying to understand probability foundations, and I find that even books do not agree, or probably I do not understand.
What I have learned:
Outcome: what can happen in an experiment. I think these are exclusive, for any experiment only one outcome not several. I think it also called "elementary event". Sample space is the set of all outcome. Example: throw the die, the outcome is 1 or 2 or ... or 6.
Event: a grouping or function(?) on the outcome. Example: the outcome is even.
Random Variable: a mapping from ___ to real numbers.
Probability: a mapping from ___ to probability, that acts like a measure (additive, ...).
The question is about the empty parts ___ above, and specifically for probability (since we can only ask one question each post).
Is probability a map from outcomes, or events? I have looked in different books and get more confused.
Book1 suggests is "outcomes": "All elementary events for a sample space. The probability of a random event is a measure on this set."
Book2: "probabilities are assigned to events"