Is this post hoc fallacy, hasty generalization, both, or something else?

P1: Harvard is one of the top schools in the world

P2: Harvard only accepts smart students

C: Therefore, if I got accepted into Harvard, I am smart

There's another variant of this argument

P1: Harvard is one of the top schools in the world

P2: Many highly successful and smart people have studied at Harvard

C: Therefore, if I studied at Harvard then most probably I am smart

The arguments are slightly different resulting the second being fallacious. The first argument is valid in that the conclusion necessarily follows from P2. P1 is superfluous (doesn't add anything to support the conclusion).

The second argument P1 is also superfluous. P2 and the conclusion have a problem with scope. "Many" doesn't necessarily mean more than half, so "most probably" cannot be concluded. This is a non sequitur . If we changed "many" to "most" in P2, the conclusion would follow.

Being tricky, someone can also say they "studied" at Harvard when they did not attend the school. I studied at Harvard. I gave a presentation there several years ago on public speaking and reviewed my notes before hand... or "studied" there. Using this trick, the fallacy committed would be equivocation (i.e., "studied" refers to "attended" in the premise and "reviewed notes" in the conclusion)... but I am smart. At least I think so.