Chance an Asian ChemE applicant for MIT, Berkeley, Caltech, etc

Run the net price calculator on each college (or have your parents do that). Any that are not affordable would be colleges where you must make the reach/match/likely/safety assessment based on a large enough merit scholarship, not merely admission. Note that many of the colleges you mention do not offer merit scholarships, so if they are not affordable on their need-based financial aid, they are out of reach and not worth applying to.

BioE is one of the most selective majors at UCB, and BioE+MET is even more selective. In addition, if the OP cannot afford out-of-state costs (UCB and UCLA do not give need-based financial aid to out-of-state students), they would need to base chances on a high level merit scholarship, which is uncommon. Therefore admission to UCB in the desired major and with a scholarship that makes it affordable would be a high reach.

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