Axioms of Probability

If $S$ is a sample space, and we have events $A$ , then probability of event $A$ happening is $P (A)$

$P (A) \geq 0$
- We can't have a negative chance of something happening.
$P (S) = 1$
- The total probability of our sample space should add up to $1$ .
If $A_{1}, A_{2}, A_{3}, \dots$ are a sequence of pairwise mutually disjoint / exclusive, $P (A_{1} \cup A_{2} \cup \dots) = P (A_{1}) + P (A_{2}) + \dots$
- Since all events are disjoint, there is no overlap or intersecting points or events in our sample space.