linear cryptanalysis: how are the subkey bits removed from the linear approximation?
So after re-reading a few times it becomes clear. The key bits are static, so they won't change the probabilities.

Now suppose that $\sum_K = 0$, then the equation in (5) will be true, with probability $\frac{15}{32}$ since it is the same equation.

Suppose now that $\sum_K = 1$, the equation in (5) is now the inverse, and it will thus happen with probability $1-(15/32).$