It may be worth recalling that the admissions system seeks to match the best candidates, chosen on merit, to the available places across the university. This is why an applicant to college X may be offered a place at college Y, or be given an open offer, which means that the applicant will be allocated to a college after the IB and A Level results are published.
I mention this to make the point that calculating things such as "college X is more likely to take a state school student", or "college Y is more likely to take a private school student" has its limitations. Any applicant could end up at any of the undergraduate colleges which teaches the subject applied for.
I suggest that applicants select as their first choice a college which they like the look and feel of, if possible after visiting a few colleges, and taking into account factors such as who is likely to be teaching at the college if the applicant obtains a place there (recognising that academic staff come and go, spend time away from teaching on sabbaticals, and so on).