Determining the probability distribution of Y. 1.) There are two urns. Into each urn is placed a set of four balls numbered, 1,2,3, and 4. A ball is randomly selected from each urn.
a.) Give the probability distribution of Y, the largest of the numbers on the two balls. 
I just can't seem to get my head wrapped around this question. A nudge in the right direction would be much appreciated.

Let $X_1$ and $X_2$ be the numbers on the balls selected from urns $1$ and $2$, respectively, and let $Y=X_1\vee X_2$. There are $16$ possible values of $(X_1,X_2)$, each of them with equal probability $\frac1{16}$. Enumerating these we find that
\begin{align}
\mathbb P(Y=1) &= \frac1{16}\\
\mathbb P(Y=2) &= \frac3{16}\\
\mathbb P(Y=3) &= \frac5{16}\\
\mathbb P(Y=4) &= \frac7{16}.\\
\end{align}
