1. If the black ball is taken out, it can't be one black and one white, only two black, because the label is wrong.

Then the inside marked with 2 black is 2 white, and the inside marked with 2 white is 1 black 1 white.

2. If you take out a white ball, it contains two whites in the same way.

Then the inside marked with 2 white is 2 black and the inside marked with 2 black is 1 black 1 white.