I started college almost 20 years ago, so I don't know the current situation. Back then the state schools had acceptance rates of only 20%-30% because so many people wanted to go to state schools to save money. There wasn't nearly enough supply to meet demand.

I never applied to any public school, but I was legitimately worried about not being accepted. I wouldn't depend on it.

I'm really glad I went to a private college in the end. People who went to state schools said class sizes were huge (like 150 students per class) and they were being taught by TAs. I really don't think I would have succeeded in that sort of environment - At my private school we didn't have any TAs and I never had a class over ~30 people, which was important because classes were very interactive.