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<p>siserune, yes I agree that the multiplicative approach works for an individual applicant, with the applicant’s personal probabilities pH, pY, and pP.
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<p>Great, but the posted question was much more specific: is that approach the only viable one — does it completely exhaust the universe of probability models that could possibly apply here, with the non-multiplicative models being nonsense? </p>
<p>Given your username I’m sure you understand exactly what the issue here is. Any model that allows correlations (i.e., non-independence of the different schools’ decisions on a single candidate) requires “spooky actions at a distance”, such as Princeton telepathically determining the admission status of Harvard candidates.</p>
<p>That actually happened a few years ago, by means that are less magical though just as entertaining. Similarly, the financial aid decisions used to be explicitly correlated until the US Dept of Justice stopped it on anti-trust grounds. Telephones and e-mail really are a form of action at a distance. But it is not likely that any of these processes are utilized for any typical applicant this decade.</p>
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<p>Indeed, there isn’t any other option available to be suggested. That’s the point. I further claim that this lack of options should be totally clear to anyone with minimal technical training in probability and statistics, and it is amazing that an AP Stats teacher would argue against independence (in what was clearly a one-applicant context) on a stats discussion list without being contradicted. </p>
<p>I’ll address your other comments about independence separately, but given that it’s been several years and dozens of repostings of tokenadult FAQ claims that the multiplicative probability calculations are “wrong”, we should make clear what is and is not the correct mathematics here. I don’t dispute that there are other sets of random variables floating around the discussion that are not independent, but it’s a separate question from the can-you-multiply matter.</p>