Taking the ratio of the areas.

The area of the ring is $4-1 =3$ times greater than the area of the circle. If the area of the circle is $1$ , then the green area is $G= \frac{2}{3}+3\times\frac{1}{3}=\frac{5}{3}$

and the red area is $R=\frac{1}{3}+3\times \frac{2}{3}=\frac{7}{3} \implies \text {the ratio of the green area to the red area is } 5/3:7/3= \boxed{5:7}$