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Response Details:
Like you said, there has to be an equal amount of black and white balls in each box for them to be independent. In other words, the probability of picking a black ball is the same a picking a probability of a black ball given box one (or box 2). In notation, we write that as: 
SO let's assume that there are 10 black balls and 10 white balls in box 1, and that there are 10 black balls and five white balls in box 2. The probability of picking a black ball in general is (10 + 10)/ (10 +10 +10 +5) = 4/7
The probability of picking a black ball given you are picking from box 1 is 10/20 or 1/2. So when there are unequal amounts of each ball in the boxes,  is false, which is a contradiction. If there are the same amount of each ball in each box, then the equation is true.
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