Probabilities & Observed Reality

StevieTNZ
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Hi there,

I'm thinking of an experimental set-up that incorporates cameras behind a double-slit screen. The cameras will take a picture if a particle goes through the applicable slit. For me to know which slit it goes through, I need to check the camera to see if its taken a picture.
For simplicity:
Slit 1 = Camera 1
Slit 2 = Camera 2

Each time a particle is emitted from the source towards the final screen, I will look at only one camera, choosing which one randomly (1/2 the time camera 1 and 1/2 the time camera 2). I emit many particles, enough to satisfy the statistics that 50% go through slit 1 and 50% go through slit 2.

How many times will I see the particle goes through slit 1 by looking at camera 1?
I know in the ideal measurement in a quantum eraser experiment (that of Scully's), 50% of those going through slit 1 are detected if we open the top shutter, and 50% going through slit 2 by opening the top shutter as well.
But what if I decided to open the buttom shutter when I could have opened the top? And the top when I could open the bottom? Would I still find 50% going through slit 1 if I still open the top shutter half the time overall?
 
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