Let's say you have two boxes labelled white and black balls in front of you. Regardless of what ball you are taking out of the bag, the generalised pigeonhole principle applies:
If there are mn+1 objects and n slots that you can put them into, then there will be at least m+1 objects in some holes. Putting into this context:
We want at least 2 objects in one of the boxes (slots). Therefore, m+1=2; m=1.
Since there are only two boxes, n=2
∴There are mn+1 objects= (1)(2)+1=3 objects, hence 3 attempts need to be made.
Hope this helps :)