Final answer:
The daughter used the 'foot-in-the-door' compliance technique by first asking for a small amount to buy a gum ball and then asking for a larger amount for more gum balls.
Step-by-step explanation:
The daughter demonstrated the foot-in-the-door technique of compliance by starting with a small request (50 cents for a gum ball) and then proceeding to ask for a larger sum ($10 for 10 bags of gum balls). This technique involves gaining a person's agreement to a small request first, which increases the likelihood they will agree to a larger request later. This is a common strategy used in various scenarios, including children's requests from parents or sales tactics in an aisle of a store.