The probability of any event $E$ is between 0 and 1:

$0 \leq P\left(E\right) \leq 1$

The probability of the entire sample space $\Omega$ (equivalently, the “certain event”) is 1.

$P\left(\Omega\right) = 1$

If for all $0 \leq i, j$ such that $i \neq j$ the events $A_i$ and $A_j$ are disjoint (i.e., $A_i \cap A_j = \emptyset$), then

$P\left(\bigcup_{j=1}^{\infty}{A_j}\right) = \sum_{j=1}^{\infty}{P\left(A_j\right)}$

In the simple case of two variables, if $A \cap B = \emptyset$ then:

$P\left(A \cup B\right) = P\left(A\right) + P\left(B\right)$