Some may try a different calculation, believing that applying to ten schools with a 10% admission rate means that there is only a 0.9^10 = 35% chance of being shut out, and that applying to fifteen of them means that there is only a 0.9^15 = 21% chance of being shut out.
But that fails to account for the following: (a) a college’s overall admission rate is not necessarily the same as that for the specific applicant, and (b) college admission decisions are not independent events like rolling a fair 10-sided die ten or fifteen times would be.