Anyone good at math (statistics) want to calculate probabilities?

Applying to College
1

<p>I guess I will begin. What are the probabilities (purely mathematical chances-not considering stats assuming that ones in the average range of each school) of being admitted to at least one school if the average acceptance rates are as follows:</p>

<p>35.2
28.0
23.3
9.2
23.0
26.8
21.4</p>

<p>I listed 7 schools. I got admission statistics from USNEWS: National</a> Universities Rankings - Best Colleges - Education - US News and World Report</p>

<p>So if some one can calculate my probability of getting accepted to one school that would be greatly appreciated. Also if you're really good at math than the probability of being accepted to two schools. </p>

<p>Also feel free to post the schools and their admission rates you guys applied to and I'm sure someone on this forum would calculate your probability of being accepted to at least one school. </p>

<p>If anyone can provide a general formula that would be really nice too. Thanks a lot.</p>

2

<p>Assume acceptances are independent of each other, which is a flawed assumption, but hey people say college admissions is random :D</p>

<p>Let p_n = probability of getting into the nth school</p>

<p>Then (probability of getting into one) = 1 - (probability of not getting into any)</p>

<p>= 1 - [(1-p<em>1)(1-p</em>2)...(1-p_n)] by (assumed) independence</p>

<p>You have an 85.6% chance if those probabilities are actually true.</p>

3

<p>this is what im learning right now...</p>

4

<p>This question is rather silly because percent admittance isn't based upon random chance, but a set of characteristics that apply to almost every college. Not everyone has a "7% chance" of getting into Harvard.</p>

5

<p>But to answer your question in the most logical way I can come up with, I would say the probability of getting accepted to one is 35.2%, which is the highest acceptance rate of the schools you listed. Even that implies that all schools use the same criteria.</p>

6

<p>there are lurking variables</p>

7

<p>It's unbelievable how often this question arises on CC. OP: your chances might be zero at all of them for all we know. It might be 100% to be admitted to at least one. Admit rates aren't just random numbers in the sky like a dice roll. They are the RESULT of people's reading through apps and allotting slots to a finite no. of applicants given the number of openings they have versus the number of applications any given year.</p>

<p>What you are asking is impossible since as several posters have already said: college admit rates are not random. If you're woefully unqualified to get into Yale (with 8.3% admit for 08) because you have a 2.0GPA for instance, you will be assured that you have zero percent with her sister colleges too -- you just can't stack admit rates and ask "what's my probability of getting into one?"</p>

8

<p>Yep, this same error in reasoning appears over and over, so often that I have written a FAQ about it (applying specifically to the case of applying to all eight Ivy League colleges, but the principles are more general): </p>

<p>APPLYING TO ALL EIGHT IVIES </p>

<p>Wrong extreme idea 1: </p>

<p>Some students "reason" that if an applicant applies to all eight Ivy League colleges, his chance of admission at any one of them is the same as the average base admission rate for all of them (which is wrong assumption a). Then the students "reason" that because the eight admission committees don't all meet in the same room, that they select students "independently" in the STATISTICAL sense (which is wrong assumption b). The students then misapply a formula learned in high school that only applies to differing situations, to calculate that the chance of getting into some Ivy League college is almost a sure thing. </p>

<p>What's wrong with wrong assumption a is that a weak applicant for admission at the least selective Ivy League college is a weak applicant at all the other colleges in the league, and that means that applicant's chance of admission anywhere is well below the base rate of admission for any Ivy League college. </p>

<p>What's wrong with assumption b is that usually colleges don't have to actively collude to end up choosing similar kinds of applicants. ALL colleges prefer stronger applicants to weaker applicants. A teacher of statistics explained to me what "independence" means in the sense used by statisticians: "What is independence? It means that when you learn about the outcome of one event, it has no influence on your guess about the probability of success in another event. However, in this case, if a student gets rejected from 8 schools, that DOES influence my guess about how likely he is to get rejected from the 9th school. I'd say someone who gets rejected from 8 schools is more likely to get rejected from the 9th than someone who didn't get rejected from 8 schools." In other words, even if colleges act independently in the layman's sense of the term, you can't use the multiplicative rule of probability to figure out the joint probability of being admitted to one out of the eight Ivy League colleges. Plenty of students get rejected by all eight. </p>

<p>Other threads from time to time bring up </p>

<p>Wrong extreme idea 2: </p>

<p>Ivy League admission officers are thin-skinned and personally offended if you apply to their "competitors," and will reject you if you apply to all eight Ivy League colleges. </p>

<p>Well, that's just ridiculous. There are plenty of students each year who are admitted to more than one Ivy League college (of course, those are rather extraordinary students) and there are at least a few each year who apply to all eight and are admitted to all eight. Ivy League colleges do NOT collude in this manner when making admission decisions. They admit the students who they think will fit well into the next entering class and contribute to the campus community. The bottom-tier Ivy League colleges admit a lot of students who don't enroll (that is, those colleges have rather low "yield,") because they admit some students who prefer to enroll at one of the OTHER Ivy college colleges that admitted them. Each college has its own tricks, in five cases including binding early decision programs, to identify students who genuinely prefer that college, but in the regular action round, every college admits some students who are also admitted by some of the other Ivy League colleges, perhaps all of the Ivy League colleges. </p>

<p>Bottom line: don't worry about either wrong, extreme idea. Apply well to all of the colleges that interest you. There is little point in applying to a college you wouldn't possibly attend if admitted, but there is every reason to apply to a college you like, because you can't get in if you don't apply.</p>

<p>Good luck in your applications. Don't use calculations that apply (well, maybe they do) to coin flips or dice tosses to guess what will happen to college applications.</p>

9

<p>
[quote]
This question is rather silly because percent admittance isn't based upon random chance, but a set of characteristics that apply to almost every college. Not everyone has a "7% chance" of getting into Harvard.

[/quote]
Exactly!</p>

<p>Now, if your GC says you have a 10% chance of getting into any of the top 20 schools and if that's all you want then anyone who got a 750 or better in math could make up a probability table for you in a second.</p>

10

<p>There's no statistical way to reliably predict admission to first tier schools. That being said, there's a binomial way to do this (with a little "fudging" changing discrete to continuous data) that gives a much smaller probability. Approximately 33%.</p>

11

<p>I'd like to agree with tokenadult. Applying to all the ivies doesn't increase your chances much - if at all. Haven't you ever noticed that someone who gets into a top school usually gets into more than one?</p>

12

<p>Actually, I would strongly disagree: applying to more Ivies <em>would</em> increase your chances of getting into at least one.</p>

<p>You are entirely right: one doesn't have any affect on the other and you certainly shouldn't depend upon published admit statistics.</p>

<p>NB: This reasoning only applies if you already have all the academic credentials – high SAT+GPA+rank.</p>

<p>However, certain intangibles aren't going to be evaluated equally. For example, one school might be looking for more students from a region of the country, while another might be overcrowded. Similarly, a certain adcomm might (for example) look especially favorably upon debaters, while another doesn't. Or maybe someone just had a bad day. The fact is: at top tier schools, there is definitely a certain amount of luck which comes into play.</p>

<p>If you really are a strong applicant, then it is worth applying to multiple top-tier colleges. Since it often comes down to luck (or an approximation thereof) whether you're accepted, it's worth playing the odds a little</p>

13

<p>This is actually incorrect because they aren't all random, but you would do this -</p>

<p>Convert to decimals (divide by 100), then subtract from 1. Multiply all together, then subtract from 1.</p>

<p>So yeah, 85.6%. But again, this is incorrect because of hidden influential variables.</p>

14

<p>^This sort of statistical analysis is NOT a reliable way to look at this.</p>

15

<p>
[quote]
I would strongly disagree: applying to more Ivies <em>would</em> increase your chances of getting into at least one.

[/quote]
</p>

<p>As stated, this statement still leaves open the possibility of getting into NONE of the Ivies after applying to all eight. I would agree that that is a distinct possibility. What applying to one more Ivy, after applying to the first seven, does is give you whatever the sheer-blind-luck probability is of getting into that Ivy. But you had that probability of getting in if you ONLY applied to that Ivy. That probability for all Ivy League colleges is less than 50 percent. </p>

<p>I agree with the proposition that sometimes hard-to-express differences make one applicant more competitive for one college than another. Some colleges, to use a familiar example, are looking for a new oboe player that year, and some are not. But to turn that around, the colleges have significant differences that matter to the students, just as students have differences that matter to colleges. Do you really want to spend four years in Hanover, New Hampshire if your idea of an ideal college town is Cambridge, Massacusetts? Is Columbia's core curriculum just like Brown's open curriculum? </p>

<p>Bottom line: apply to the colleges you like. Apply to a safety college </p>

<p><a href="http://talk.collegeconfidential.com/college-search-selection/493318-dont-forget-apply-safety-college.html%5B/url%5D"&gt;http://talk.collegeconfidential.com/college-search-selection/493318-dont-forget-apply-safety-college.html&lt;/a> </p>

<p>for sure. Don't count on getting into any college more speculative to get into than your sure-bet safety college. (And apply to your safety college early on in a rolling admission process, if at all possible.)</p>

16

<p>Maybe applying to all the Ivies would increase your chances, but then again, isn't it pointless to apply to a college just because it's an Ivy? For example, I'm not applying to Dartmouth because it's a fairly small place, and I like to be in the centre of everything. I know that I wouldn't really be happy there. And even your safeties should be the kinds of places that you'd genuinely like to study at.</p>

<p>Suppose I get into Dartmouth, but not any of the other Ivies. What then? I choose Dartmouth over some other colleges I might be happier at just because it's an Ivy? It's not worth it in the end - prestige will only take you so far.</p>

17

<p>I think we're on the same page tokenadult.</p>

<p>First and foremost, you need the qualifying stats. You also need realistic expecations: even strong students have distinct possibility of getting into no Ivies.</p>

<p>Honestly, I don't buy the whole "fit" thing though. Maybe it's just me, but I have the attitude that college should <em>push</em> you outside of your comfort zone. I grew up in a rural area, but I'd be just as happy in downtown NYC or the middle of nowhere.</p>

18

<p>If we're talking location here, it's not about the kind of place someone grew up, IMO; every freshman is going to have to deal with change, and the kind of location is no exception. It's about where they'd personally prefer to stay, where they think they'd be happy at. By the time someone is college-age, they should have at least a rough idea of their likes and dislikes.</p>

19

<p>I'm sorry but Tokenadult nailed it.</p>

20

<p>
[quote]
^This sort of statistical analysis is NOT a reliable way to look at this.

[/quote]
</p>

<p>I know. Please read that I said that it was incorrect.</p>