If completing WaniKani means mastering 975 N1 kanji out of 1232 (79.14%) while let’s say 12 kanji is required to understand the context of each question, then the chance to success in JLPT N1 is:
Not sure if you’re serious, but a lot of the “missing” N1 kanji are quite rare. I never encountered them on the actual test. Lists of kanji for the levels are crude estimates.
Also you seem to not be counting any kanji from N5-N2. All those kanji obviously continue to get used on N1.
There’s also a lot more to JLPT success than raw kanji knowledge.
If it was meant as a joke, then ignore me.
I just reminded of how latent efforts often discouraging due to no visible result. When realizing that not knowing a single kanji on the same level might make it impossible to solve a question, I try to calculate that factor. It’s also a reminder for me to not force myself attempting N3 when I still not acquired enough kanji for it.
Love the idea behind the post. For the sake of taking it too seriously, replacing the constants based on the 144 joyo kanji missing (based on wkstats):
WK kanji: 2136 (this is higher than the standard joyo because I think jinmeiyou kanji are included here)
Total: 2280
keeping r as 12
gives about 45.6%, which sounds like a closer ball park. You could argue r should be smaller, and there’s a lot of conditionals not taken into account here like frequency and vocab knowledge. But is a fun idea!
You’re assuming kanji to be way more important than they are in your calculations.
My kanji/vocab score on the N1 was abysmal. I went in having formally studied maybe ~1200 kanji total and I stopped studying them all together over a year before I took the test. I also had studied less than the 10000 words that get thrown around a lot and I studied only 50% of the words on the old N1 list. Going by those numbers, I should have miserably failed. But I didn’t. I got a comfortable pass. (Scored 136/180.)
Like Leebo pointed out, the N1 isn’t made up of purely N1 kanji. Pretty sure they are the minority, with the lower levels being much more frequent. Because of this, the number of 12 N1 kanji required to answer a question correctly is much too high for the vocab/grammar questions, and I don’t think the math works at all for the reading/listening questions. For reading, not understanding a certain word (even one that comes up a lot) is much less of an issue than one first assumes. For listening, kanji don’t matter for obvious reasons.
Also, you’re not actually calculating the “chance to succeed” but the “chance that you know enough kanji to potentially answer a question correctly”. You can still get the question wrong (because of other things like lack of grammar) or right (because of luck). Additionally, you don’t need to answer every question correctly to get a pass on the JLPT.
Btw, you can write the same thing using latex and markdown
\Pi_{i=0}^{r-1}\frac{n-i}{k-i} = \frac{n-0}{k-0} \times \frac{n-1}{k-1} \times ... \times \frac{n-(r-1)}{k-(r-1)}
n is amount of kanji learned for the JLPT;
k is amount of kanji involved in the JLPT;
r is amount of kanji required to understand the context of a question.
\Pi_{i=0}^{12-1}\frac{975-i}{1232-i} = \frac{975}{1232} \times \frac{974}{1231} \times ... \times \frac{964}{1221} = 5.95%
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