when you are talking about precipitation, you need to think about the solubility of specific salts.
different salts have different desires to dissolve, and via Le Chatelier's principle, you can think of adding Pb2+ ions as adding "product" of dissociation to the system. in reaction 3, they added PbI2 into a mix which had CO3(2-), so what you ask yourself is "Which one has a greater molar solubility, or which one is better at dissolving, PbCO3, or PbI2. judging by reaction 2, the Pb ions happily left Iodine and bound to CO3, where they precipitated out. that means PbCO3 is worse at dissolving then PbI2.
if you have a good understanding of Acid base chemistry, this can be compared to adding protons to a solution of Cl- ions and H3CCH2O- ions (deprotonated ethanol). in that situation, you ask, which is the stronger acid, HCl or Ethanol? definitely HCl, so for the system to reach equilibrium, it will leave the stronger acid dissociated and allow the proton to protonate the Ethanol. (thats qualitative, but once you get to the Solubility you'll notice a system analogous to ka and pka exists for salts, Ksp.
hope that helps some.
