What are the odds of someone ping their finger through a solid wall?

Since matter does not really touch other matter but what we see and experience is electrons repelling one another, if you somehow lined up the electrons in your finger so they avoid the ones in the wall you could p through it if only for a second. I wonder what the statistical probability is that when one goes to make contact with the wall at least some of one's own atoms actually enter the wall (so that the electrons are lined up just right on those atoms that there is enough space).