Electrons have negative charge, and therefore repel each other. That should mean that their position, and momentum probabilities should get skewed away when in the presence of some other electron. I.e. probabilities of them being close together should be very low.
So, if we send in two electrons at a time towards the slits, the probability that they passed through the same slit should be pretty low. Now I have two questions :
$1)$ What happens if we detect the electrons at one of the slits? If we see only one electron enter that slit, then the other electron must either have gone through the other slit, or not gone in. Does interference still occur?
$2)$ Why do electrons interfere anyway. In the two electron case, they should repel each other, and therefore their interference should greatly decrease, right?