Box Ball Logic Problem

Question

There are three bags.

1. The first bag has two blue rocks. 
2. The second bag has two red rocks. 
3. The third bag has a blue and a red rock.

All bags are labeled but all labels are wrong.You are allowed to open one bag, pick one rock at random, see its color and put it back into the bag, without seeing the color of the other rock.

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

Solution

Just one!

You pick a ball from the bag labelled "blue and red" ... if its blue then that's the 2 blue rocks bag and likewise for the red. ( since all bags are labelled wrong the one reading blue and red would not actually contain a blue and red ball. So it label will be whatever color of ball comes from it) Next if we get a blue ball from the blue and red labelled bag we know that the bag labelled red has got to be blue and red since we have already used up the blue label and since all bags are labelled wrongly it cannot be red.