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Should be "getting in and being able to afford to attend" (i.e. with sufficient scholarships and/or financial aid if one cannot pay list price).>>>
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Definitely true for us, @ucbalumnus! We’re not even putting on our list any of the “high reach” schools or really ANY school that does not offer merit aid since we know we won’t get much if any need-based aid. No Harvard for my kid even if she COULD get in. 
(It’s all good - she doesn’t want to go to any “fancy” school that has a super competitive vibe anyway.)
There are 0% chances. Examples:
- School has no merit scholarships. School's list price is too expensive for the student. Student has wealthy parents who will not pay, or will not cooperate with financial aid forms.
- Student does not meet a hard minimum requirement either in high school course work or grades/scores. An example would be students wanting to attend a CA or SD public school as frosh but do not have an art class or accepted equivalent in their high school record.
Fair enough. How about this: assuming you meet the hard minimum academic requirements and can afford to attend the school, there’s never quite a 0% chance.