I have a Venn Diagram that looks like this:
$$A) \, 213 \quad B) \, 160 \quad A\cap B) \, 100$$
The items from $A$ come from a population where their probability to be selected is $\frac{313}{12800}$.
The items from $B$ come from a population where their probability to be selected is $\frac{260}{1407}$.
How can I calculate a null model that tells me the number of shared items expected by chance if I create a Venn diagram for that data?
If $A$ and $B$ were independent, you would expect the same fraction of $B$'s to have $A$ as the whole population. Of the $260 B$'s, $100$ are also $A$'s, about $38\%$. But of the whole population, $A$'s are rare-a little less than $4\%$. Similarly the other way around. They are far from independent.