Also, the admission decisions of different colleges are not completely independent events, since many criteria (high school courses and grades, test scores, etc.) are considered by many colleges. So assessing probabilities as if they were independent events may not give an accurate estimate, even if realistic (as opposed to overly optimistic) estimates are used.
In addition, it is not just the chance of admission that needs to be estimated; it is the chance of admission and affordability. Admission to a college that is too expensive is like a rejection. If the student needs a merit scholarship to be able to afford the college, the chance estimate needs to be based on the scholarship, not merely admission. However, this is often much more difficult to estimate than for admission if the scholarship is competitive (as opposed to automatic for stats).