Why Do Ag+ Ions Replace Na+ Ions in NaCl Solution?

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Lets say I have a solution of NaCl and decide to add some AgNO3. I know a white precipitate will form so obviously some Ag+ ions have dropped their NO3- counterparts and combined with Cl- ions instead. Why does this happen? Is it all to do with electronegativity? Is it a simple matter of Cl- anions being more electronegative than NO3- anions and Ag+ cations being more electropositive than Na+ cations?
 
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When these things dissolve in water, you have an equilibrium, e.g.:
NaCl <--> Na+ + Cl-
Salt is quite soluble so obviously that equilibrium is shifted pretty heavily to the right most of the time.

So your dissolved salts are continuously dissolving and reforming, and in different combinations. As it happens, AgCl is relatively insoluble, so the equilibrium:
AgCl <--> Ag+ + Cl-
Is shifted to the left.

So the ions don't go back into solution much. That's what 'insoluble' means.
 
Does electronegatively play a significant role in this?