[shard]

Not sure if the OP is the author, or if the author will read this, but I ate the shed, and at first found it delightful, but then got an annoying bit stuck in my teeth.

The Guide first says "The results of the spell are supposed to be independent." And I took that at face value, since I figured this is an educational page rather than a page of brain teasers and trick questions. But then when it asks "in my last 100 casts of the spell, I got the gross potion all 100 times, what do you think the next cast would yield?", I guess I was supposed to have remembered that the original statement said "supposed to be independent", and figure out the lesson was that this indicates a problem with the spell not being independent as opposed to stressing that regardless of results, independent means independent. I feel annoyed rather than enlightened.

[giomasce]

My problem with that question is that it seems to imply that of something has a very small probability to happen, then it cannot really happen. This is false. The probability of me generating my precise GPG or writing this exact comment were ridiculously small before these events happened, and still they happened.

Or, from another point of view, it's worthless to ask what is the probability of something that has already happened. Once something has happened (i.e., if you constrain to that thing having happened) its probability is one, full stop. You have to ask a question before running the experiment.

[eternalban]

That's not really correct. There are more bits of information regarding the event of your comment than the spell. It was observed you read the GP. Your profile is read, interests noted. Your comment history gives us probability of your making a comment today. All in all, pretty sure a much higher probability than "very small" in the sense that you intended it.

[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."

[necovek]

Yeah, another problem is that none of the answers offered at that question is really "right" according to the adventure. I also find it contradictory. If you did "cast a spell" a 100 times, and recorded that sequence, and then asked what's the likelihood of getting any particular value after getting exactly that sequence, one could argue similarly that there's only a 1/2*100 chance of the previous sequence happening (yet it just did for the author), so something must be wrong with it. Basically, they are saying that some of outputs are not equally likely, and I am now seriously confused.

This is such an early point to attempt to highlight features in purportedly random behaviour that is not really random.

It didn't annoy me, it just made me quit at that point, especially as I was already battling the spell terminology.

[motoxpro]

I had the exact same experience. Stopped right then and there. Great concept though and awesome work!