A faculty leader was meeting two students in Paris, one arriving by train from Amsterdam and the other arriving by train from Brussels at approximately the same time. Let $A$ and $B$ be the events that the respective trains are on time. Suppose we know from past experience that $P(A)=0.93, P(B)=0.89$, and $P(A \cap B)=0.87$. Find $P(A \cup B)$.
$$P(A \cup B) =P(A)+P(B)-P(A \cap B)=0.93+0.89-0.87=0.95$$