# Relationships between sub-samples with limited information

I'm doing an analysis where I've been able to assemble the following information about a population, its overall conversion rate (so, the percent of the members of that population who go on to make a purchase), and the conversion rate of one particular subset of the population.

What I want to know is, how can I find the conversion rate of the full population minus the known subset?

Put another way:

Full Population x : n = 3,000,000, conversion rate == 0.6%

Subset y : n = 52,000, conversion rate == 2.6%

Subset z (z here == x - y) : n = 2,948,000, conversion rate == ???

I know I can make up a dummy dataset that matches these characteristics, but it seems like the sort of thing that has, that must have, a more elegant mathematical solution.

• Why not just do the math? It's perfectly elementary: subtract the subset count from the population count and subtract the subset conversion count from the population conversion count. Divide one by the other to get the rate. – whuber Jun 29 '17 at 19:38
• @whuber - aha, so, use the existing conversion rate for x to determine the total buyers / non-buyers, and then math it out. – Toof Jun 29 '17 at 19:46