A Problem on Probability

Two cards are drawn randomly from a pack of 52 well-shuffled playing cards, one after one, without replacement. Suppose the event $A$ is the two cards are of the same suit while the event $B$ is one of two cards, or both, is a Jack, Queen or King. If $P(A \cup B) = \frac{u}{v}$ where $u$ and $v$ are positive integers and $\gcd(u,v)=1$ , find $u+v$ .