Probabilities out of non-normalizable functions?

[AshIsH_0001]

Homework Statement

There is an electron gun placed at (x,y)=(0,0) in some coordinate system. At x=1nm there is a
screen with two small holes in it, at y =±1 nm. At x=2 nm there is another screen with three holes in it, at y =±1 nm, and at y =0 nm. There is a movable detector placed at x=3 nm. The amplitude for going between points r1 and r2 is given by (notice that this is not normalized):
(See the solution attempt)
(a) Draw a picture of the system. Write down an expression for the probability of finding an
electron in the detector using Dirac notation.
(b) Assume that we have a detector which always lets us know wether or not en electron went
trough the hole at (x, y)=(2, 0). How does the expression for the probability change with this
knowledge?
(c) If the electron is shot out with a momentum of 10 e.V./c, what is the probability of detecting it
at y=0? Use the above equation for the amplitude and use the fact that it only depends on the
distance between two points in order to simplify your expression.

Relevant Equations

<r2|r1> = (e^((i/h)p.r21)/|r21|

a and b were fairly easy to solve; but the c part which actually demands the probability! How are we suppose to fetch the value if the function can't even be normalized; I tried to make some assumptions like making the system bounded; but I don't think that it's the right way to do so... What can be the correct approach? What is the best assumption we can make using the conditions provided??

Would be grateful if anyone could provide me some guidance; any insigth to confirm if I was right from the start for a and b parts would be appreciable...

 

[anuttarasammyak]

Oberve the small area S on the screen including y=0. Say n particles hit S in total N particle bombardment.
Then we can estimate the value
\frac{n}{SN}
which is probability per unit area.
Could you show us the non-normalizable function you get for investigation ?

 

[AshIsH_0001]

Oberve the small area S on the screen including y=0. Say n particles hit S in total N particle bombardment.
Then we can estimate the value
\frac{n}{SN}
which is probability per unit area.
Could you show us the non-normalizable function you get for investigation ?

How can i just calculate the required probability at the detector when placed at (3,0); i tried to solve but ended up some very complicated equations which isn't that easy to solve for probability densities...