<p>I'm just trying to get a handle on the problem of lots of people applying to lots of the same schools.</p>
<p>Hypothetical problem:</p>
<p>There are ten top colleges which can each accept 1000 freshmen.</p>
<p>There are 10,000 applicants, all equally qualified, who each apply to all 10 top schools, thus the acceptance rate at each of these colleges is 10%.</p>
<p>Theoretically, there is space for all 10,000 students in these schools.</p>
<p>What is the chance that a particular applicant will be accepted at NONE of these colleges?</p>
<p>Or put another way, how many students of the 10,000 will be rejected everywhere?</p>
<p>My (non-statistics) thinking: The chance of being rejected from one school is 0.9 (90%). For two schools it's 0.9 times 0.9, or 81% chance of being rejected from both. So for 10 schools, the chance would be 0.9 times itself 10 times? That would be 38.7%. Is that possible? That would mean that even though there is space for all in the freshmen classes, that almost 4000 students out of the 10,000 would be rejected EVERYWHERE???</p>
<p>In order for your math to work the events (rejection) need to be statistical independent and truly random. Unfortunately, I don’t think there I’d such thing as equally qualified students or true statistical randomness in college admissions</p>
<p>You have set this up so that the “expected” number of acceptances per applicant equals one (assuming statistical independence of decisions). Many students in your example would be accepted to more than one college, however, and some would be accepted to none. The upshot is that the acceptance rate would have to be above 10%.</p>
<p>Given the assumptions, the probability is 0.9^10, which is 0.349. (I think you used .9^9=.387 ). However coase is correct that the school would have to accept more than 10%, knowing that the yield was going to be more like 650 students/1000 acceptances, rather than 1000/1000. And of course Munequita is most likely correct that the events aren’t statistically independent and random.</p>
<p>If there were only 10 schools, and only 10,000 qualified applicants, all the students would end up admitted to one of the schools–even if it was from the waiting list.</p>
<p>Of course, the real world situation is much more complicated. There are many more than 10 schools completing for top students, students don’t apply to the same mix of schools, and schools look at different criteria for what they consider “qualified.”</p>
<p>But yeah, the more schools you apply to, the greater your chances of being admitted to at least one–as long as you have some chance of being admitted to any of them.</p>
<p>I’ve seen the calculations before. The problem is that the rates are not fixed in that there are students who have different acceptance rates, ie special situations. Which affects the general acceptance rate as well since that is built into the calculation. The model would work if a computer selected the students in a purely mathematical way, but that is not how colllege admissions works.</p>
<p>It wasn’t a real world question… It just sometimes seems that you’ve got lots of people picking colleges for prestige only, and they will apply to many of the top-tier schools, even though the schools might be quite different from each other. By being so “unselective” in school choice, they contribute to the chances of lots of qualified students not being accepted at those schools.</p>
Not really. If a student applies to college X, gets accepted, but doesn’t go there, another student will go instead. Indeed, the colleges calculate this and accept more students than they have space for. If they still don’t get enough, they just go to the waiting list.</p>
<p>When discussing statistics I find it useful to reference Shakespeare:</p>
<p>There are more things in heaven and earth, Horatio,
Than are dreamt of in your philosophy.</p>
<p>-- Hamlet from Hamlet, Act 1 Scene 5</p>
<p>Munequita hit the problem on the head. Your question/answer assumes independent & random decisions. You’re essentially assuming that all aspects of a candidate’s application are equal and valued on exactly the same level by all schools. Unlikely.</p>
<p>Having said that, it wouldn’t surprise me if 34.5% of candidates applying to all the top 10 schools got rejected by all of them. Like the riddle of the Sphinx, Stonehenge and the relentless popularity of anything Kardashian, coming up with a truly accurate formula for predicting college admissions appears to be beyond the ken of mere mortals.</p>
<p>If you mail marriage proposals to Scarlett Johansen, Kirsten Dunst, and Gwynneth Paltrow, what are the odds one of them will accept? Will your odds increase if you add Taylor Swift and Kelly Clarkson?</p>
<p>That’s a good analogy, Hunt. What appeals to one starlet in a mate may be of little interest to another. </p>
<p>For there to be a mathematically viable formula in the OP’s question, you would have to assume that all the qualities of the “equal” candidates are valued with equal weight by each institution. Since that is a false premise with regard to colleges, no statistical probability can be determined based on the given information.</p>
<p>^^^ That’s what I’m thinking. Buying two tickets doesn’t double your odds of winning the lottery, right? It means you know have two 1 in a billion (or whatever) chances of winning.</p>
<p>^^^Ummm, actually buying two lottery tickets with different numbers does double your chances. If there are 100,000,000 possible combinations and you have 1 ticket your odds are 1 - 100,000,000. If you have 2 tickets with different numbers your chances have “improved” to 1 - 50,000,000. That’s because there are a finite number of possible outcomes. I can’t comment on your chances with Scarlett Johansson, though I recommend sticking to lottery tickets.</p>
<p>And, in light of the typical April posts, the probability that all of the 4,000 rejected students happen to be discriminated Asians is … 98.11 percent, rounded up from 98.1056565.</p>
<p>“Ummm, actually buying two lottery tickets with different numbers does double your chances.”</p>
<p>However buying 2 lottery tickets in 2 DIFFERENT lotteries does not increase your overall chances of winning any one lottery.
The college admissions process is like buying tickets in multiple lotteries. The chances of wining in one state has no impact on the chances of winning in another.</p>
<p>the same goes for applying to colleges[ statistically speaking]</p>
Well, not exactly. In the real world, we know that it’s very difficult to predict who will be accepted to any specific selective college. That is, one student might be accepted at Harvard and rejected at Yale, while another student might have the opposite result, and you can’t discern why from the outside. So, a student who wants to go to Yale or Harvard–and has credentials that make acceptance plausible–will increase his chances of getting into at least one by applying to both. We can’t tell how much it increases his chances, though.</p>
). However coase is correct that the school would have to accept more than 10%, knowing that the yield was going to be more like 650 students/1000 acceptances, rather than 1000/1000. And of course Munequita is most likely correct that the events aren’t statistically independent and random.</p>