Quark Quartet Fuels Quantum Feud

This story highlights one of my favorite logical paradoxes of quantum mechanics. Quantum mechanics rely on applying some very sophisticated probability analysis. Every statistical analysis has a real, finite, non-zero uncertainty in the predictions of what can and cannot happen. How can quantum mechanics then claim something cannot or must happen. Both claims have an uncertainty of zero.

In a double-slit experiment, what is the probability that a photon will not pass through both slits, ie, will pass through one slit or the other only?

The experiment that still rattles my brain is the single electron, double slit experiment. In this often repeated experiment, individual electrons at a current flow rate of about one electron a second go toward a double slit. The electrons that make it through presumably one or the other slit gets detected by hitting a phosphorous screen and a pulse of light is observed. [Other detectors have been used but this method is so dramatic.] Single, discrete electrons clearly leave the gun and reach the screen. When one looks at a sum of the location distribution, the typical double slit distribution appears. Somehow these individual electrons interfere with themselves.

I still cannot wrap my head around this.

Err, hold on, here's an extra quark for Muster Mark.