Probability Measure is Monotone

Theorem
Let $\EE$ be an experiment with probability space $\struct {\Omega, \Sigma, \Pr}$.

Let $A, B \in \Sigma$ such that $A \subseteq B$.

Then:
 * $\map \Pr A \le \map \Pr B$

where $\map \Pr A$ denotes the probability of event $A$ occurring.

Also see

 * Elementary Properties of Probability Measure