@merc81 I took the premise that @ucbalumnus gave as being that you could estimate “your personal chance of admission at each one”. Even if you can do that then it is not “routine to complete the math (and answer the original question) once probability values (however they may differ from general acceptance rates) have been assigned to each of the ten schools” because you cannot simply multiple these 10 probabilities together.
@MWolf is making the same mistake of assuming that you can simply “multiply the chances that an applicant has to be accepted at each college, given their stats and profile. That will provide the probability that they will be accepted to at least one college”. It won’t. Lottery tickets are not the right example to use because the probability of each individual ticket winning is independent (so the “joint probabilities” are not relevant). The best example is the 2016 election forecasts where you had estimates of the probability of the candidates winning each state, but you couldn’t just multiply them together.
As Nate Silver noted (https://fivethirtyeight.com/features/a-users-guide-to-fivethirtyeights-2016-general-election-forecast/):
“The error from state to state is correlated. If Trump significantly beats his polls in Ohio, he’ll probably do so in Pennsylvania also. Figuring out how to account for these correlations is tricky, but you shouldn’t put too much stock in models that don’t attempt to do so. They’ll underestimate the chances for the trailing candidate if they assume that states are independent from one another.”
That’s a good explanation of why this calculation (even if you could estimate the probability of getting into each college or winning each state) is “tricky” rather than “routine”.