If the labels are all incorrect, you would want to start with the one labelled with the drink you don't want. This would give you an initial chance of 75% of g

If the labels are all incorrect, you would want to start with the one labelled with the drink you don't want. This would give you an initial chance of 75% of getting the drink you do want (.5 + .25). If you don't get it on the first press, then you would press the one labelled "random", as this would 100% be the drink that you do want.