testing my Pearson

Hi there.. I just registered because I'm becoming desperate and I hope someone will know an answer to this one.. :) I'll make this more picturesque.
I've got a huge array of size N, with green and red numbers which can be either 0 or 1. The red numbers are quite rare. The ones (number=1) are quite rare too. I've calculated a Pearson correlation coefficient between reds and ones and it's around -0.6 meaning a somewhat negative correlation between ones and reds, ones are mostly green. What statistical test can tell me if that correlation has some relevance, that it's significant, or it's just accidental because there's a lot of greens anyway so of course ones are mostly green? So, I'm searching for a method which can tell me if my correlation is or isn't crap :eek: I hope the problem is clear :wave: