If I understand you, you’re saying that this simplified calculation should give the same answer as the full calculation, and that this should be obvious to me after I try it both ways.
But you’re also saying that the simplified calculation is equivalent to the earlier problem with only 1 owner, which means I already worked it both ways (one way in the 1-owner problem and the other way in the 2-owner problem) and I got different answers. So, no, the equivalence is not obvious after running it both ways.
My suspicion is that this half-remembered theorem you are trying to apply actually applies to a different situation and you are using it wrong. But if you don’t think that’s the case, then yes, I’d like to see a more precise explanation. (And ideally, an explanation of what you think I did wrong in my own calcs.)
If I understand you, you’re saying that this simplified calculation should give the same answer as the full calculation, and that this should be obvious to me after I try it both ways.
But you’re also saying that the simplified calculation is equivalent to the earlier problem with only 1 owner, which means I already worked it both ways (one way in the 1-owner problem and the other way in the 2-owner problem) and I got different answers. So, no, the equivalence is not obvious after running it both ways.
My suspicion is that this half-remembered theorem you are trying to apply actually applies to a different situation and you are using it wrong. But if you don’t think that’s the case, then yes, I’d like to see a more precise explanation. (And ideally, an explanation of what you think I did wrong in my own calcs.)