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.