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Let's say you have 10 groups of members. Each group can have an arbitrary number of members, but let's keep it clean (unless it matters?) and say each has 10,000 members. Between the combined memberships of any given two groups, there's a 10% overlap (meaning, 10% of the members will belong to both groups). Since we're assuming a membership of 10,000 per group, that means the distinct membership would be 18,000 between two groups.

Problem: What is the distinct total count of members, in aggregate across all 10 groups? And how/why?

This seems like it should be easy, but I can't figure it out for the life of me. Thank you!

Vlad
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Vlad
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  • Need to add the self-study tag. – Michael R. Chernick Nov 22 '19 at 00:55
  • This does not have a unique answer. It depends on how members shared between two groups may or may not be shared between the other groups. More generally, you [cannot get the joint distribution of $n$ variables by considering the pairwise marginals.](https://stats.stackexchange.com/questions/305067/get-joint-distribution-from-pairwise-marginal-distribution) – Him Nov 22 '19 at 01:45
  • Thank you, Scott, I appreciate your help. That makes sense, and explains why I was struggling so much with the problem conceptually--it's not solvable. – Vlad Nov 22 '19 at 02:25

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