I have to question whether you're trying to prove GPs point, as this is hilariously incorrect. Unless you're using very unlikely values for easy and/or small.
Firstly, you're assuming independent probabilities between the students.
If it's a single class of 30, for certain skills it might be much more likely than pow(0.5, 30) if they were all specifically coached on that particular skill, or if there are selection effects impacting what type of person ends up in that group of 30.
Secondly, even if we grant the assumption of independence, the claim doesn't rely on "unlikely values for ... small". There's many small towns with a student body of only 5 or less people, and pow(0.5, 5) isn't that unlikely.
The probability is just pow(0.5, N) where N is the student population, assuming that the distribution has no skew, assuming independence between students, and assuming the students are drawn randomly from the general population. It's an exponentially decreasing function, so it becomes incredibly unlikely for large student bodies under these assumptions.
I disagree with this argument, but that's the basis of it.
I have a basic understanding of statistics and a basic understanding of logical fallacies, and I deal with this kind of sounds-good-if-you-don't-think-too-hard "insights" all the time.
Perhaps an intermediate understanding would help. Entire schools tend to score higher or lower together, also wealth correlates to IQ and scholastic success and zip code. There are also other reasons an entire group would be biased higher or lower.
> I deal with this kind of sounds-good-if-you-don't-think-too-hard "insights" all the time
Now I'm thinking of a horror fan fiction version of lake wobegon where they give all kids an IQ test at a young age and murder all those below the national average.
Just my crazy version of what "easy" could entail.
