Final answer:
AGI is more soluble in the presence of CN- because it forms a soluble complex with CN-, which overrides the common ion effect that would normally reduce solubility due to the presence of a common ion.
Step-by-step explanation:
AGI is less soluble in water than in a solution that contains CN- because AGI forms a complex with CN-. This happens due to a chemical process where the silver ion (Ag+) tends to form a two-coordinate complex with cyanide ions (CN-), which is a soluble complex in water. This phenomenon goes beyond the common ion effect, which would predict lower solubility in the presence of a common ion. Instead, the formation of a soluble complex explains why AGI is more soluble in the presence of CN- ions.