Answer :
AgI should precipitate first.
The concentration of
when CuI just begins to precipitate is, 
Percent of
remains is, 0.0076 %
Explanation :
for CuI is 
for AgI is 
As we know that these two salts would both dissociate in the same way. So, we can say that as the Ksp value of AgI has a smaller than CuI then AgI should precipitate first.
Now we have to calculate the concentration of iodide ion.
The solubility equilibrium reaction will be:

The expression for solubility constant for this reaction will be,
![K_{sp}=[Cu^+][I^-]](https://tex.z-dn.net/?f=K_%7Bsp%7D%3D%5BCu%5E%2B%5D%5BI%5E-%5D)
![1\times 10^{-12}=0.0079\times [I^-]](https://tex.z-dn.net/?f=1%5Ctimes%2010%5E%7B-12%7D%3D0.0079%5Ctimes%20%5BI%5E-%5D)
![[I^-]=1.25\times 10^{-10}M](https://tex.z-dn.net/?f=%5BI%5E-%5D%3D1.25%5Ctimes%2010%5E%7B-10%7DM)
Now we have to calculate the concentration of silver ion.
The solubility equilibrium reaction will be:

The expression for solubility constant for this reaction will be,
![K_{sp}=[Ag^+][I^-]](https://tex.z-dn.net/?f=K_%7Bsp%7D%3D%5BAg%5E%2B%5D%5BI%5E-%5D)
![8.3\times 10^{-17}=[Ag^+]\times 1.25\times 10^{-10}M](https://tex.z-dn.net/?f=8.3%5Ctimes%2010%5E%7B-17%7D%3D%5BAg%5E%2B%5D%5Ctimes%201.25%5Ctimes%2010%5E%7B-10%7DM)
![[Ag^+]=6.64\times 10^{-7}M](https://tex.z-dn.net/?f=%5BAg%5E%2B%5D%3D6.64%5Ctimes%2010%5E%7B-7%7DM)
Now we have to calculate the percent of
remains in solution at this point.
Percent of
remains = 
Percent of
remains = 0.0076 %