Well how can you disagree with them? You said you have no information on the number of balls in the box and yet your proposed method is implicitly assuming that there are *exactly* two balls in the box. If you aren't willing to assume anything at all then this is just unsolvable. Now if you're asking about how you could do this in practice and you had some way to mark the balls before you replaced them back in the box then you could estimate the number of balls in the box and in turn estimate your probability of interest. If you are willing to maybe put a distribution on the number of balls you believe could be in the box you could use that to in turn put a distribution on what you believe the probability to be (this is very Bayesian in flavor but since we aren't collecting any data we would basically just be relying on prior distributions the whole time).