## Probability of hitting a target

I've been trying to work out the probability of hitting a spot in the center of a target and running into some snags.

The problem is this:

There are two target circles. One has a 10.5 meter radius and 1.3 sigma spread inside of that radius while the other has a 16.5 meter radius and a 2 sigma spread inside that radius. Both have a linear progression through to the edge of the target, but from there things are truncated and there is only a 2% chance that all throws will miss the target area.
The question is what is the probability of a throw hitting a 9x7 rectangle in the center of the target.
As a side note, x and y are calculated independently and then plugged into the formula to determine where they land.

I was doing just a linear interpolation, and that puts both about the same, but it doesn't take into account the truncated probabilities (1.3*9/10.5 and then looking up that z value). I was thinking that I would have to take the probability out of 1.3 or 2 plus .02 and then dividing the calculated z value by that.

Would this be accurate or am I chasing butterflies in the field on this one?

Thanks.