Multiballs I

Question

You have two urns in front of you, say $1$ and $2$. Urn $1$ has $m$ red and $n$ blue marbles inside, while urn $2$ has $n$ red and $m$ blue marbles inside. Assume that $m,n \geq 1$. You select one urn uniformly at random and select $2$ marbles uniformly at random without replacement. In your selection, you observe $1$ red and $1$ blue marble. Find the probability that you drew from urn $1$ when $m = 7$ and $n = 4$.