Mislabeled Boxes of Marbles

Three closed boxes have either white marbles, black marbles or both and they are labeled white, black and both. However, you’re told that each of the labels are wrong. You may reach into one of the boxes and pull out only one marble. Which box should you remove a marble from to determine the contents of all three boxes? 

 Mislabeled !

Find here how it can be done!  

Source 

Correcting labels of Marble Boxes

How they were mislabeled? 

We should pick marble from a box labeled as 'Both'. Since it is incorrectly labeled it must content either all black or all white marbles.  After we know what it contains, we can identify the other 2 boxes by the process of elimination as below.

1. If the marble picked is BLACK, then obviously it is the box of black marbles. Two remaining boxes labelled as WHITE & BLACK are left. Since all labels are wrongly tagged the box tagged with WHITE must not be the box with all white marbles. It must contain both colors of marbles. And the one tagged as a BLACK must contain all white marbles.
 
Look at the figures below. In circle, labels are written & outside are the contents of the boxes. Arrows represents how the contents are rotated to make labels of the boxes wrong.

2. If the marble is WHITE, then obviously it is the box of white marbles. Two remaining boxes labelled as WHITE & BLACK are left. Since all labels are wrongly tagged the box tagged with BLACK must not be the box with all black marbles. It must contain both colors of marbles. And the one tagged as a WHITE must contain all BLACK marbles.