@ucbalumnus Yes, if the probability of acceptance to an individual college is zero, adding that college, whether correlated or not, to the set obviously won’t improve the joint probability. Applicants still need to find colleges that “fit”. Assuming s/he can find a number of colleges that “fit”, s/he should apply to a subset of these colleges that maximize the joint probability while minimizing the amount of resources required, instead of applying to every one of these colleges or to a less than optimal subset.