What statistics to use to find a possible correlation of coinciding null results?

I would like your advice on the following problem:

I am investigating the following data: For 600 trials data was gathered simultaneously from two sources (locations in rats brain). Each trial was investigated and either a result was found (some time stamp) or no result was found (a "zero result"). I call the fraction of "zero results" found in source 1 X1 and in those in source 2 X2. What I want to investigate is wether these zero results coincide more often than is expected from their individual fractions. If there is no correlation in found zero results we expect to find coinciding zero results in P=X1*X2 of the cases.
To calculate the chance of finding the number of coinciding zeros that were actually find I am currently using the binomial cumalitive distribution function (using the binocdf command in MATLAB http://www.mathworks.nl/help/toolbox/stats/binocdf.html).
Here I use N=600, X= found number of coinciding zero's and P=X1*X2. So far so good, if you disagree on using this method please let me know.

However I actually have 5 sources (5 locations), meaning I can check for correlations in all combinations of sources (10 in total). I would like to combine the statistics on all these combinations into one number which gives me the probability of finding the number of coinciding zero's under the assumption that there is no correlation (i.e. that P=x1*x2). Do you have any advice on a good (and hopefully easy) method? This is just a little sideline I am investigating and the results need not be accurate to the 10th decimal.

Thanks in advance for any help/advice