If I apply to 10 highly selective universities, each with a ~10% admission rate (universities like Duke, UPenn, UChicago, etc.), and I am an "average" applicant to each of these universities, is it probable that I will be accepted to at least one of them?
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Since each of these universities has a 10% admission rate, and I am applying to 10 universities, the expected value is admission into one university. Since the "average" applicant to each of these universities has a 10% admission chance, and there is randomness in admissions, wouldn't this be true?
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Answer:
Take the variable X as the no. of universities you get into Defining success as getting selected by a university, your probability of a success 'p' = 10% or 0.1, and probability of failure 'q' = 90% or 0.9 The probability of K successes (getting selected by K universities) is given by: P(X = K) = First, let's see the probability that you get selected by at least 1 university: P(X = at least 1) = 1 - P(X = 0) = i.e. there is a 65.13% chance that you get selected by at least some university Now, let's calculate the expected no. of universities you get selected by . This is given by: E(X) = (i.e. for each possible value of X from 0 to 10, multiply X with the probability of getting into X universities, and add them up) This works out to 10*p = 10*0.1 = 1, i.e. the expected value of the number of universities you get selected by is 1 Note that this is no guarantee of getting into a university. It just shows that you have a decent chance. EDIT -- Of course, all of this assumes that selection is purely random and a student has 10% chance of getting in. This is completely different from " a 10% admission rate", which implies that 1 out of 10 people who apply get selected. In reality, if you're "average", it is highly unlikely that any of the universities will consider you among their top 10%.
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Other answers
Those students that make you think "how in god's name did this person get in this school?!?!?" have to come from somewhere, so yeah, your logic is flawless.
Neil Barackinator Gottel
Not quite. In a perfect world, the colleges will be admitting the top 10% of applicants, not picking 10% randomly out of the pool. If all applicants had the same chance of being admitted, then yes, you would expect to get into 1/10. It gets a bit more complicated if you take into account imperfect admissions criteria. If the applicants to a college are on a bell curve and you are right in the center, chances are you won't be admitted. Correct me if my logic is wrong!
Daniel Fang
I don't think the "average" applicant at any of these selective schools has more than a microscopic chance of being accepted anywhere, so applying to 10 of them will not do much to improve your odds. It's only when you get into the viable-contention range that your probability begins to quickly rise with multiple independent trials. Let's say you're exactly at the 50th percentile line in all qualifications. That means for any trait -- GPA, test scores, leadership roles, etc. -- there will be 4 applicants more qualified or more accomplished than you at each individual institution. The stars would really have to align perfectly in order for your unique combination of these same attributes to put you over the top. You were Student Government President? So were 30,000 other students throughout the nation, thousands of them co-applicants to the same handful of elite schools. Unless you have a strong hook -- are a star athlete, come from a prominent family, or are a severely underrepresented minority -- or have some highly unusual accomplishment, you will most likely get weeded out in the initial pass. Why would the admissions staff spend lots of time pondering over the details of the bottom two-thirds to three-quarters with slim odds when the remaining one-quarter to one-third have all the same attributes at even higher levels of accomplishments? Their job is not to give YOU the fairest chance, it's to build the best composite class by the announcement deadline date. If you do well enough to survive the initial culling, however, then random chance comes more into play: At one school, you are the first rodeo clown they've seen for awhile; at another yours is the third similar applicantion they read that year. Each admissions committee is trying to fill multiple goals: they look for applicants from all 50 states; they tally totals for URMs, Pell Grant recipients, and first generation college students and look at gender balance. The more of these elements they can check off with a single candidate, the more likely that a given candidate will be given the nod. They will consider your record to see if you are likely to participate in their popular extracurricular clubs and organzations. These are the intangibles where random chance occurs and where multiple applications can truly be considered independent trials. I think the suggested strategy is best applied to a portfolio of schools where your personal stats place you close to the top quarter. However, if you are an extremely lopsided candidate -- say an Olympic contender or national prize winner with a low-ish GPA or SAT score due to your non-academic focus during high school -- then you should apply to as many selective schools as time allows because you always have a shot at being a one-factor acceptance candidate.
Roland Priebe
A simple probabilistic analysis, such as you and most (but not all) of the answers consider, embodies the tacit assumption that the ten acceptances/rejections are independent, which is not the case here. A more complex probabilistic analysis would require quantifying the dependencies and correlations, which we don't have the information to do.
Richard I. Polis
Your question could come under the rubric of the Monte Carlo Fallacy. Each time you apply to school with a 10% acceptance rate you still only have a 10% chance for each one. The odds of your getting in donât improve mathematically. While what I have said may be accurate, there are at least a couple ways you can improve your chances of being admitted. Look over your list of schools and pick the one or two that are your top choices. Not the ones that are hardest to get in but the ones that match your interests. Apply to at least one of them early action/early decision. The acceptance percentage of students who apply to the most selective schools goes up, in some cases dramatically, when the student applies early. Some schools permit you to apply early action to more than one school. Some donât. Early decision is limited to one school and if you are accepted you must enroll. For you top schools you should think of ways that you will stand out. For example U Penn (a school that does take a much higher percentage of student early than regular), the specific question they ask to applicants this year is why Penn. Most answer ths question talking about rankings and great education, but often it is abstract and not specific enough to stand out. If you do some significant research on the school, professors, programs and you can convince Penn admission readers that you are in the top 10% of those who know what they can and will do there, this may increase your chances for admission. Any time you can âproveâ you want to go to a school because of a passion for learning in specific programs or working with specific professors you have demonstrated that you are know the school and want to go there for the ârightâ reasons.
Parke Muth
Say highly selective school X gets 18,000 applications, and of those, half are from applicants school X would *love* to accept. By the time school X has narrowed the field from 18,000 to 9,000 applications, grades and scores aren't in play, because all 9,000 could succeed academically at school X, and have grades and scores that rock, or other stuff that makes school X very happy with the grades and scores they do have. So all the nonnumerical factors now come into play. Not all the 9,000 who didn't make the cut missed on numerical factors. The 4.78 weighted GPA, 2390 who "failed to interview" at the interview, and whose essays show no personal whatever whatsoever, is gone. So are lots of other numerically enormously qualified applicants. All that's left are completely gonzo, loveable applicants. Picking 1500 of the 9,000, any 1500 of whom would make a great class, is an incredibly subjective exercise. So this leads to my view, substantiated to some extent indirectly by discussions I've had with admissions officers, but still my own essentially unsubstantiated, offbeat view, that if you would make it to the gonzo, loveable remnant at all ten schools, and if, at each of the ten schools, so would about nine applicants for every admission the school has to offer, even if it's the same pool across all ten schools, there will be a sufficiently low coefficient of correlation in admissions from one school to the next that your chances of being admitted to at least one of the ten schools are significantly higher than your chances of being admitted to any particular one of them. Are your chances three times as high? Five? It's a conceptual point, and I have no way to quantify it, but if I were applying to schools today I would apply to as many schools as I thought reasonably likely to consider me gonzo loveable, etc., as I could. Note "average" won't cut it. But the student who clearly would make it into that "love to take them all" pool at most top schools will do well to apply to a bunch - a carefully chosen bunch being best, to be sure, but still it's worth augmenting that one dream "I've just got to go there" school with eight or ten more that are just as dreamy.
Thomas Glen Leo
You misunderstand statistics. If each school has a 10% admission rate and you are average for that school it doesn't mean that you have a 10% chance at that school. You might have a 3-4% chance. Additionally percentages are not additive. If I flip a coin once the chances of head or tails on a non biased coins is equal...50%, the next flip is equally equal. If you say what are the chances or two heads in a row it becomes 25% (.5*.5). Each university is a separate coin flip. You are average to them so your chance is not average, they offer more to better students and their yield is not that great as some have different preferences or chose better schools. So you may have a 5-10% chance of getting in or greater/less depending what the schools are looking for.
Christopher Fox
Would you date someone who is more attractive than 90% of people (top 10% of attractivenss? OKCupid found in their analytics that a man in the top 5% of attractiveness, as rated by women on the site, gets twice as much interest in online dating as the men in the top 10% of attractiveness. Even though the top 10% is deemed attractive, the top 5% gets twice as much interest in dating. What that means is that the very, very top students âthe "unicorns" â are going to be sought out by every school they apply to. The students that get accept to all eight Ivies, yep, they count in the top 10% admissions rate at all eight of those schools... The good news is it only takes one acceptance to be a success (same as dating). Work on displaying your best qualities, and you might increase your attractiveness in the eyes of one of the admissions committee. The math you were trying to do works for random, independent probabilities. College lotteries aren't a raffle, though. Just because you have a 0.00001% chance of a selected person making it to the NBA in any one season of play doesn't suggest that Lebron is going to statistically lose that lottery year after year like the rest of us. The fact that he won the NBA lottery once and beat the odds once is an indicator that his chances of being in the league for another season are far greater than the rest of us with more normal basketball talents. If basketball teams had a college admissions process, he'd get selected to all of them.
Taylor Hall
That depends. Are you average in just grades and scores and extracurricular activities, or are you truly average among their applicants? What's missing from most "average accepted student" data is the intangible stuff that actually determines whether you get in. Grit, passion, overcoming hardships, going above and beyond, being really unique, etc. Good schools want student bodies full of interesting and passionate people, not just a bunch of robots who get good grades and score high on tests. If you're boring, it's entirely possible to apply to 10+ elite schools with perfect grades and scores and get denied by every single one of them. If you're able to convince them you have something special, you could apply with below average stats and get into all of them. When I applied to college, I applied to 2 schools - University of Chicago and DePaul (which I never had any intention of attending but my parents insisted I choose something "more realistic"). I got into both and went to Chicago. Due to some issues back home, the first couple years were rough and I ended up taking some time off before applying to Wash U in St. Louis with sub-par college grades. I got in there, too. I never applied anywhere else. I suspect my success rate in admissions was due to the fact that I really played up the things that are harder to quantify. If you've had setbacks or traumas, find a way to show how you overcame them. If you have an interesting passion, play it up. If you know exactly what you want to do and where you're headed, show them what that is and how their specific university factors into that. If there's anything that SHOWS you're more motivated and determined than the average elite student, include it. Don't just say you're passionate and leave it at that. It's like storytelling - show, don't tell. I know it's a stressful thing and there's a tendency to want to simplify it or make sense of it all. Just give up on that idea. There's no score or grade or number of applications that will guarantee you a spot at a top school. If you're average in scores alone, I'd recommend applying to as many top schools as you can while still making your applications really good.
Stefanie Hutson
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