Atop a high shelf are three bins. You know that each of these bins contains dozens of colored ping pong balls. These balls are all colored either black or white, however, the shelf is too high for you to actually see inside a bin. You can however, reach with your hand and pull a ball out of a bin and see what color that individual ball is.

Each bin has a label on it. These labels read "Black Balls," "White Balls," and "Mixed Colors." You are told that indeed there is a bin which has only black balls, one with only white, and one which is mixed, however, ALL of the labels on the bins are incorrect.

By only drawing balls out of the bins, what is the minimum number of draws you would need (and how would you do it) to determine the correct labeling for the bins?