The first box has two red balls. The second box has two green balls. The third box has one red and one green ball. Boxes are labeled but all labels are wrong! You are allowed to open one box, pick one of its balls at random, see its color and put it back into the box (you do not get to know the color of the other ball). How many such operations are necessary to correctly label the boxes?

A classic puzzle.

Since no label is correct, we have to distinguish between two cases: (GR is labeled GG, GG is labeled RR, RR is labeled GR) or (GR is labeled RR, RR is labeled GG, GG is labeled GR). So pick one ball at random from the box labeled GR.