A number of websites offer tools which estimate odds of being accepted to universities given grades and standardized test scores, based on applicant data. The question of calculating odds of getting into at least one university given their acceptance rates has already been asked, but as mentioned in the comments for that question, the events are not independent, because all acceptances are dependent on scores. Given acceptance rates after factoring in scores, can a more conclusive statistic be calculated?
Example:
Say a student is applying to three schools, $a$, $b$ and $c$, with $A$, $B$ and $C$ representing acceptance into each school respectively as events. Factoring in test scores, $P(A)$ is 54.9%, $P(B)$ is 24.87%, $P(C)$is 19.95%. What is the probability of getting into at least one school? Two? All of them? Confidence intervals?
Moveover, what impact does the quasi-dependence have on the results?
Not enough information given. For instance if the universities have the same rule for admission that your grades are $\geq t_i$ for some threshold $t_i$ for individual university $i$ then the probability to get into one will be $\max(P_i)$ the same as probability to get into the easiest one.