Multiple if and if not in list comprehension

I tried to look at similar questions but I'm really not understanding how I can accomplish this using the methods mentioned in the other questions. So my problem is: I have one list from which I want to remove certain values. For instance:

a = [[[0,0],[0,1]],[[0,0],[0,1]]]
for y in range(2):
    a[y][:] = [x for x in a[y] if not random.random() < s]

This removes the elements for which random.random() is below s (being s between 0 and 1). However, I only want this to happen if the second position of each element of the list (that is the [0,0] bit) is equal to 1. I tried multiple solutions (suggested around here for other questions) and I can't get it to work. Does anyone have any suggestion?