Precipitation of Cu2+ and Pb2+ ions Hi chemistry enthusiasts!
I am working on my scholarship exam practice. I believe this exam assumes high school + first year university knowledge although the standard may be varied across the world. And I'm not quite sure what I did wrong. Could you please have a look?


  There is an aqueous solution containing Cu2+ and Pb2+ ions. The most
  suitable reagent to precipitate one of the two ions from the solution
  is (1) nitric acid (2) sodium carbonate (3) sulfuric acid (4) hydrogen
  sulfide


I picked answer (4) hydrogen sulfide because I think that it will react with copper (II) ions and will precipitate out. However, the correct answer is (3) sulfuric acid. How is this answer correct and what did I do wrong for hydrogen sulfide. Your advice will be much appreciated!
If you read the question carefully, they wish to precipitate only one ion, either copper or lead. The facts that must be in your mind are:

(i) Lead sulfate is insoluble in water but copper sulfate is.
(ii) Both lead sulfide and copper sulfide are water insoluble.