[jerf]

I think that's a really hard problem to phrase correctly no matter what you do, because no matter what you do, you're swimming upstream against almost the entire mathematical education that person has had up to that point. Up to that point the answer to "Susie has 37.8 cookies and wants to split them evenly weighted by the body mass of the 17 people in her class, how many cookies does each person get?" has never been "Why the hell does she want to do that?" But that's the kind of answer you're fishing for at that point.

No criticism intended of the question itself. Every stats course should have it in there somewhere, it's a very important one. But I'v personally tried my hand at how to phrase it exactly right a couple of times and it's really, really hard.

(Since this is an invitation for 50 people to post their attempts, I would also point out it's easy to phrase it in a way that works for you, who wrote the question. You might find if you take it out for testing that it doesn't work as well as you thought, though. But by all means, smash that reply button. I can't stop you. :) )

[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."