Can a dumb person study at cambridge university?

Why do you ask? You applyin'?

Many dopey people in high up jobs, I’ve certainly met a few.

Came away thinking “A rich mommy and daddy must go a long way, because you’re a fucking idiot.”

I depends on how you define dumb, or rather to what connotation of dumb you're referring.

Depends on what kind of stupid.

Lots of dumb people do

If you are a bankers child or something yes

I would assume that it would take a lot of luck and a lot of money.

Yes, but mostly no. Unless you're a prince or something and get your placement because of said reason then there's no way you could get there on your own abilities.

Like others have said, it depends on what way in which they're dumb. There are a lot of very book smart people with not a lick of common sense. I have known many highly educated people like this, and I was amazed they could even manage to dress themselves in the morning.

They can study there but they can't attend or get a degree from them.

Clearly yes!

Most anyone not in the student population can get a library pass and study whatever they want to in many of the buildings on any College/University campus in America.

Most anyone can register for a limited number of classes without any specific education background as well (as long as you can pay the fees).

Full time enrollment is a different question. The Colleges and Universities have standards for that - and depending on how dumb or in what way they were dumb they may or may not be able to be a full time student.

Prince Charles attended Cambridge, which is proof that there was a time when someone who wasn't that bright in academic terms could get in if they had the right name and connections. There's a persistent story that Charles's personal bodyguard, who attended all the seminars and lectures that Charles did, took the final exams at the same time as Chucky, and the bodyguard's results were better. I don't know if that's true, but it seems entirely plausible to me.

But that was back in the sixties, and both Oxford and Cambridge have done a lot in the decades since to try to ensure that only the very brightest students are allowed in. In the UK, there isn't the system that exists in the USA where the offspring of graduates of a university get extra brownie points during the admissions process, and nor can a billionaire build a new golf course or some other sporting facility for the university and that will guarantee that their dim-witted spawn will be granted entry and given a free ride until they get their diploma.

Prince William apparently wanted to go to Oxford, but he didn't get good enough results on his A-Level exams (the closest American equivalent to those are Advanced Placement exams). He ended up attending St Andrews University, which is more or less the Scottish equivalent of Oxford and Cambridge.

People can study anywhere. No one is born smarter or dumb.