[necovek]

The focus of the question should not be on the independence of the probability, at the very least: you are setting a responder up for failure, and that rarely leads to satisfaction. Perhaps the only problem is with the given response: if it was "Yes, BUT..."

If you expect the "why the hell does she want to do that", you can't ask that in a quiz form. Why the hell are we collecting potions: I couldn't care less, right? And then you suspend your disbelief, and then suddenly, "uh-uh, that's too unlikely, you should have questioned your assumptions."