PikaPika999

The answer is $\sqrt{913}$.

I will post explanation soon it is very long:

To find the denominator, we have to find the total number of ways to choose the marbles. There are 13 ways to choose the first marble and 12 ways to choose the second marble, so the denominator is $13\times12=156$.

To find the numerator, we have to find the number of ways that the first marble is green and the second marble is red. There are 7 ways to pick a green marble and then 6 ways to pick a red marble, so the numerator is $7\times6=42$.

This means that the answer is $\frac{42}{156}$, which simplifies to $\boxed{\frac{7}{26}}$.

By the way, our usernames are very similar 

Wait, but @ikleyn, check out my answer here:

Let $y=f(x)$, so $y$ can take on any value from $-3$ to $5$, inclusive. Then, $y^2$ can take on any value from 0 to 25, inclusive. )If we take any value from $-3$ to $0$ and square it, we get a value from 0 to 9. And if we take any value from 0 to 5 and square it, we get a value from 0 to 25.) Therefore, the range of $g(x)$ is $\boxed{[0,25]}$