Present data quantity I have some data on widgets. Each widget has a universal identifier (ID), which I can use to compare data (from various sources) about the widget. I have data from some sources, and I wanted to see the quality of the data that a potential additional source (Foo) might supply me with. So I sent Foo a sample of widget IDs from my database. Foo sent me data on some of my widgets, but didn't have data on all of them.
How can I estimate the number of widgets that Foo has data on and I do not? (I expect that answers will depend on any or all of these counts: all IDs, IDs that I have data on, IDs that I sent Foo, IDs that Foo sent me data on, IDs that Foo has data on. It might also depend on domain knowledge, but please try to estimate without that, and indicate precisely where it will be most useful.)
 A: My first thought: the number of widgets Foo has that you do not might follow a hypergeometric distribution. 
Notation
Using Wiki's notation, $N$ would represent the total size of their data, or the number of IDs they have information about. 
$K$ would represent the number of IDs that they have information on, that you would like, because you don't have info on them. These are the possible "successes." 
Finally, $n$ is the number of times you ask them for information. Each request could come back negative, if you already have it in your data, or if they don't have info for that one. Or it could come back positive, they have some new data for that ID that you haven't seen before. 
Answer
You say, "[h]ow can I estimate the number of widgets that Foo has data on and I do not?" This is equivalent to point estimation of the parameter $K$. This parameter is integer-valued. Implementing something like maximum likelihood estimation would be complicated by this fact. 
Let $k$ be the number of times they got back to you with good IDs you needed. Assume you know $N$ (you ask them how big their dataset is) and $n$ (the number of IDs you requested info for). Write a function that evaluates the likelihood, or pmf for the parameter $K$:
$$
L(K) = \frac{{K \choose k} {N-K \choose n-k} }{{N \choose n} }
$$
Then loop over $K$, and return the the specific one that gives you the largest likelihood. 
