Chapter 8.4, Problem 37E

In Problems $37$ and $38$, urn $1$ contains $7$ red and $3$ white balls. Urn $2$ contains $4$ red and $5$ white balls. A ball is drawn from urn $1$ and placed in urn $2$. Then a ball is drawn from urn $2$.

If the ball drawn from urn $2$ is red, what is the probability that the ball draw n from urn $1$ was red?