Show that if one event A is contained in another event B, then P(A) _< P(B). Hwat does this imply about the relationship between P(AUB), P(A), and P(A inersect B)?
If each of $\displaystyle C~\&~D$ is an event then $\displaystyle C \cap D = \emptyset \; \Rightarrow \;P(C \cup D) = P(C) + P(D)$.
Consider this: $\displaystyle B = A \cup \left( {B\backslash A} \right)\;\& \;A \cap \left( {B\backslash A} \right) = \emptyset $.
So, $\displaystyle P(B) = P(A) + P(B\backslash A) \geqslant P(A)\text{, because }P(B\backslash A) \geqslant 0$