self Maths Puzzle

The first box has two white balls. The second box has two black balls. The third box has a white and a black ball.

Boxes are labeled but all labels are wrong!

You are allowed to open one box, pick one ball at random, see its color and put it back into the box, without seeing the color of the other ball.

How many such operations are necessary to correctly label the boxes?

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self Other Question

Place 10 balls in 5 lines in such a way that each line has exactly 4 balls on it. At a restaurant, how could you choose one out of three desserts with equal probability with the help of a coin?

Bonus: What if the coin is biased and the bias is unknown?