Therefore, I can easily build a 2x2 contingency table using as variables the presence/absence of A and B.

And I can apply a chi-square test on this table, building an "expected" contingency table, to asses the independency of both properties.

But I also need to assess if the number of cells that "overlap" (are true in both matrixes, i.e. where both A and B are present)

**is higher or lower than expected**if both properties were independent. Of course I can compare values between the real and the expected contingency tables, but what I need is some thing like a probability or a measure of how overlap is higher or lower than expected. In some way, it can also be seen as a measure of the "correlation" between both properties?

I know if I had a smaller number of cells I could use Fisher's exact test, where obtained p-value will indicate the "direction" of the relationship between A and B. But as Fisher's exact test implies factorials, it is not possible.

There is another simple test (preferably if it is easy to program in a language such as C#) I could use for this aim?

Thank you very much for any help!