# Percolation Theory Basics: Open cluster size decay (Square Lattice)

I am trying to learn some stuff about percolation. On wiki (http://en.wikipedia.org/wiki/Percolation_theory) it says:

"when $p<p_{c}$, the probability that a specific point (for example, the origin) is contained in an open cluster of size $r$ decays to zero exponentially in $r$."

... which suggests that we are very likely to be in a small cluster, but less and less likely to be in an increasingly large cluster. (I think)

I am slightly confused by this. In the picture below are clusters on a $1000$x$1000$ square lattice (site percolation, where $p_{c}=0.592...$) and the image was made when $p=0.58$, so $p<p_{c}$.

However, if you look at the image, most of the area is taken up by large clusters. So if we take a specific point on the grid, surely we're most likely to find that it is in one of these large clusters?

Can anyone explain what I am misunderstanding here?