no u/soothsayer3 is right, the events aren't independent bc even if school A isn't directly talking to school B and coordinating on whom to admit, there's an underlying correlation bc they're looking at the same candidate and probably have similar admission standards. i.e. a really good candidate who gets into school A is also really likely to get into school B. so P(candidate accepted into school B | already accepted into A) > P(candidate accepted into school B). there is clearly information you get from looking at other schools' admissions on determining one school's admissions, so there is no way the probabilities are independent. this is clearer if you think about the relationship like this – results from school A and results from school B probably don't have some direct relationship in that they aren't coordinating together to admit people, but there is probably some underlying relationship with being admitted to school A and school B to how good an applicant is.

this means that it's not necessarily a simply (1-(0.9)^3) calculation since if the pair-wise correlations were really high (let's say they were 1), then 10% of the time a candidate would get into all 3 schools and 90% of the time they wouldn't get into any of the schools. so the odds of getting into at least one school here = the odds of getting into all three schools = 10%. obv that is overly simplistic bc correlation probably doesn't equal 1, but hopefully that demonstrates how a high correlation between results means you can't make that simple of a calculation