Can you solve the "scrambled box tops" puzzle?

Here's a puzzle from Martin Gardner's Mathematical Games column, which ran for many years in Scientific American. I found it in his anthology, My Best Mathematical and Logic Puzzles, which is only $3.76 on Amazon.

Imagine that you have three boxes, one containing two black marbles, one containing two white marbles, and the third, one black marble and one white marble. The boxes were labeled for their contents – BB, BW, WW – but someone switched the labels so that every box is now incorrectly labeled. You are allowed to take one marble at a time out of any box, without looking inside, and by this process of sampling you are to determine the contents of all three boxes. What is the smallest number of drawings needed to do this?

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