third quiz is up

The third quiz is up. The first quiz, as its title suggests, deals with topics found in BOE (Bad Online English) Units 1 through 5. The second quiz deals with topics from Units 5 through 8. The third quiz deals with Units 8 through 13.

That's all I have for now. I'm gassed out. What a weekend.

Please don't move on to a subsequent quiz until you're getting at least an "A" on the previous quiz. If I could build in something to prevent students from moving on—like Khan Academy, which has established hurdles that you must clear before you can advance—I would do so. Maybe I can ask ChatGPT to add that code, but that might require students to register and have a student number. Right now, with the way things are, all scores are private and not recorded anywhere. With the Khan Academy system, students have to register; I assume they get a student number, and their performance is recorded and tracked. I'm not nearly that ambitious yet, and if I were, I'd study to become a web designer. No, I think the current relaxed format is good for casual students who are looking for a challenge.

As mentioned before, you can garner partial credit for all questions. The people have spoken. While ChatGPT didn't code each answer choice as a, b, c, or d, what it did do is give each answer choice its own check box. Each answer for each question is worth 1/4 point. Simple as that. Unlike typical multiple-choice questions, where you have a 1 out of 4 chance of getting a question right, my multiple-choice questions can have any number of correct answer selections, from zero to one to two to three to four. In the end, though, only one answer configuration is correct out of all the possibilities. And how many possibilities are there?

Any of the following are possible ways to check the squares:

Possibility 1 ☐☐☐☐ nothing checked

Possibility 2 ☑︎☐☐☐ one checked

Possibility 3 ☐☑︎☐☐ one checked

Possibility 4 ☐☐☑︎☐ one checked

Possibility 5 ☐☐☐☑︎ one checked

Possibility 6 ☑︎☑︎☐☐ two checked

Possibility 7 ☑︎☐☑︎☐ two checked

Possibility 8 ☑︎☐☐☑︎ two checked

Possibility 9 ☐☑︎☑︎☐ two checked

Possibility 10 ☐☑︎☐☑︎ two checked

Possibility 11 ☐☐☑︎☑︎ two checked

Possibility 12 ☑︎☑︎☑︎☐ three checked

Possibility 13 ☑︎☑︎☐☑︎ three checked

Possibility 14 ☑︎☐☑︎☑︎ three checked

Possibility 15 ☐☑︎☑︎☑︎ three checked

Possibility 16 ☑︎☑︎☑︎☑︎ all four checked

...and only one of the above is correct per question.

(On the quiz, the check boxes are aligned vertically.)

So unless I've counted wrong, every question has 16 possibilities—for idiots who are merely guessing. For people who know the right answers, there's only one possible answer set per question. So you can try to guess your way through the quiz, but you probably won't pass via random guessing. ChatGPT calculates the chance of passing via random guessing as 

__________

About 13.16%.

Why: each quiz has 5 questions × 4 options = 20 option-states to match (checked vs. unchecked). If someone blindly guesses each checkbox independently with 50/50, each option has a 0.5 chance to match its correct state. So the total number of matches is Binomial(n=20, p=0.5).

“Passing” on your scale means ≥64% of 5 points = ≥3.2 points. Points come in 0.25 steps, so the minimum passing total is 3.25 points = 13/20 matches. Thus:

$$P(\text{pass})=P(X\ge 13),\quad X\sim \text{Binomial}(20,0.5) = \frac{\sum_{k=13}^{20} \binom{20}{k}}{2^{20}} \approx 0.1316.$$

P(pass)=P(X≥13),X∼Binomial(20,0.5)=220∑k=1320​(k20​)​≈0.1316.

So a pure coin-flip guesser passes about 1 time in 7.6.

(If someone uses a non-random “strategy” like leaving everything unchecked, the probability depends on how many options are actually false that round. The 13.16% figure is for true random guessing on each checkbox.)

__________

(I don't have the math to verify GPT's calculations, but I'll trust it for now.) So, guessers, you have a small chance, about 13%, but you'd be better off studying. Or take the quizzes relentlessly over and over again, memorizing the correct answers to every question you encounter... but by that point, you'll have been learning the grammar I've been teaching, so it won't be cheating.

And get this—cheating is an anagram of teaching. That means nothing, but whoa.