I agree that if the number of Ivy Leaguers is realistic, then it's not trope-worthy. But I think that even in elite prep schools and professions, it's unrealistic to depict everyone as having (or wanting) degrees from schools like Columbia, Cornell, and Dartmouth, if there's barely any mention of schools like Duke, Rice, or Johns-Hopkins. (The latter universities aren't Ivy League, but they're just as competitive and prestigious as many of the Ivies.)

This trope isn't about improbability- it's about "went to an Ivy League school" being used as shorthand for "this person is very smart". Now, the number of Ivy League graduates we see in fiction is improbable- the freshman admission of all the Ivies put together is probably less Florida State, but this is incidental for reasons that I'm going to explain in the write-up since that's actually a very good question and this information should be in the article.

Ironically I first became aware of this trope from a review of the Gossip Girl book series in which the reviewer, an Ivy League grad, wrote to the effect that the girls were far too socially focused and spent far to little time on school work to be a realistic portrayal of someone even considering an Ivy League education. I have never read the books or seen the TV show, so I can't say if this is true or not. But I will say that the only person from my high school class who went to an elite private school (in the midwest, not an Ivy) was smart enough to have to study little for A's, but spent her free time working on science fair projects, quiz bowls, learning to play french horn, mock trial club, etc. and went far beyond what the students who went to the state flagship did (which itself is one of the nation's top 10 public schools) did.

If this isn't about improbability I think the title should be changed. Because every work page I've seen that features this page has it used to show the improbability.

The improbability is a side-effect of the smartness it is meant to show.

It's like IQ tests. IQ tests are generally bell-curved with SD 15 and Mean 100. So when some character has an IQ of 180, it is supposed to have the viewer go "Ah! He's smart." The probability of getting a 180 on an IQ test is extremely low, so it signifies smartness/uniqueness/specialness/etc. The same thing applies for this trope.