Shooting a single photon through a double slit Consider the image below. It shows a double slit experiment but with a single photon at a time. My question is as follows:
Why is it that the photons always take a different path when shot at the same target? Where does the uncertainty lie? If we shoot it in exactly the middle of the two slits, why does it have a 50-50 chance of going into either slit? And why is the amount of diffraction for a single photon always different?
I know that people will say that the photon enters both the slits at the same time and things like that. But does anyone have an intuitive explanation as to why this happens? Why does a photon, shot with the same frequency and exactly in the same direction, still have the probability of entering either slit. Why is it that the diffraction of a single photon is different for the same wavelength?
So in brief, why does a single photon which is shot in an exactly the same why as the previous one, end up being in a different place. I am looking forward to an answer with the least possible math (if any). Or is it that a photon cannot be shot in the exact same way as the previous one?

Image source: http://abyss.uoregon.edu/~js/images/photon_double_slit2.gif
 A: The photons do not have a well defined trajectory. The diagram shows them as if they were little balls travelling along a well defined path, however the photons are delocalised and don't have a specific position or direction of motion. The photon is basically a fuzzy sphere expanding away from the source and overlapping both slits. That's why it goes through both slits.
The photon position is only well defined when we interact with it and collapse its wave function. This interaction would normally be with the detector. If we interact with the photon, to define its position, before it reaches the slits then the diffraction pattern disappears.
A: The problem with the picture (and probably with your understanding of the physical process) is that it assumes photons as classical particles on well-defined trajectories. If this were a true picture of reality, your objection would be justified. This, however, is not so. 
In order to describe the process properly, one has to acknowledge the quantum nature of the photon. Quantum mechanics tells us that particles do not have well-defined trajectories, one can only make statements about probabilities, which in turn can be calculated from their wave function. So if you have a system like the double slit where probabilities for the photon going through each slit are equal, one cannot make a definite statement about what will happen, not even if you have just a single particle.
To clarify this even further, one can also think think about it in terms of the Heisenberg uncertainty principle: it is not possible to determine momentum and position simultaneously. A well-defined momentum implies large uncertainty in position.  
A: "I am aware of the QM and wave particle duality. All I want to ask is that can you you shoot a photon towards a single target which probably is not possible."
And
"@JonCuster I understand your point and thanks for the advice. Just one last bit. Can I therefore say that it is impossible to shoot a photon at the exact same point as the previous one?"
Ok, so this is the real question.  And the answer is yes, you can fire two photons at the same point.  It's trivial.  Point a laser pointing at the wall.  However, using a laser pointing you can't reproduce the experiment that you mentioned.
