You clearly don't know who you're talking to, so let me clue you in. I am not in danger, Skyler. I am the danger. A guy opens his door and gets shot, and you think that of me? No! I am the one who knocks!

The Correct answer is 1. The lowest number of marbles that can be picked to determine the correct contents of each box is one (1).

Explanation:
Since each of the three boxes are incorrectly labelled, then the incorrectly labelled box labelled as Mixed or as Black/White, will actually correctly contain either 2 Blacks OR 2 Whites. Therefore to correctly determine the contents of each box one simply needs to go no further than to pick a ball (one ball) from the box that has been incorrectly labelled as Mixed or Black/White. Now, assuming the ball picked is Black, we then already know that that box is supposed to be labelled BLACK. Again, for the other two boxes to be incorrectly labelled in this scenario the one incorrectly labelled BLACKS will contain 2 whites and the last box incorrectly labelled WHITES will correctly contain Mixed marbles or Black/White.
Also, assuming the ball picked from the incorrectly labelled box labelled as Mixed was white, then the box incorrectly labelled white will correctly contain 2 BLACKS and the last one will contain the Mixed marbles. (This of course is the way its done without having a look at the contents of the box). FINISHED !!!