Admissions Probability ?

Pneumatic
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Admissions Probability ?

Postby Pneumatic » Mon Dec 27, 2010 3:56 am

All things being equal (softs, etc.), if a person applied to 4 different schools, each of which, statistically, he had a 25% probability of being accepted at, is it likely (statistically) he would get accepted to at least one of those schools? It appears to me that probability theory suggests he should; however, it also kind of seems unlikely. Does normal statistical theory apply to Law admissions as represented in this post, or would it differ in some way for some reason?

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IAFG
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Re: Admissions Probability ?

Postby IAFG » Mon Dec 27, 2010 3:57 am

no one ever really has a 25% chance.

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Ragged
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Re: Admissions Probability ?

Postby Ragged » Mon Dec 27, 2010 4:04 am

Pneumatic wrote:All things being equal (softs, etc.), if a person applied to 4 different schools, each of which, statistically, he had a 25% probability of being accepted at, is it likely (statistically) he would get accepted to at least one of those schools? It appears to me that probability theory suggests he should; however, it also kind of seems unlikely. Does normal statistical theory apply to Law admissions as represented in this post, or would it differ in some way for some reason?


I sorta doubte that. Even if you could know what your exact probability is (which you can't), I'm pretty sure that's not how these things work.

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Nulli Secundus
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Re: Admissions Probability ?

Postby Nulli Secundus » Mon Dec 27, 2010 4:11 am

Besides, admission to each school is an independent event, as in, your admission or rejection any one of them does not affect your chance of admission for other schools. Thus, adding the probabilities together is just dumb. Its like saying, there is a 50 percent probability of heads in any coin toss, ergo, if I toss a coin 2 times, I will definitely get a heads result.

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Re: Admissions Probability ?

Postby 09042014 » Mon Dec 27, 2010 4:11 am

If he had 25% at four schools, and each schools chance was totally independent from the other it would be 69% likely that he'd get into at least one.

The problem is that it isn't independent, and law school admissions aren't totally random.

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Re: Admissions Probability ?

Postby Pneumatic » Mon Dec 27, 2010 4:13 am

nullisecundus wrote:Besides, admission to each school is an independent event, as in, your admission or rejection any one of them does not affect your chance of admission for other schools. Thus, adding the probabilities together is just dumb. Its like saying, there is a 50 percent probability of heads in any coin toss, ergo, if I toss a coin 2 times, I will definitely get a heads result.


You should statistically get heads at least once if you flip a coin twice. Wow...

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straxen
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Re: Admissions Probability ?

Postby straxen » Mon Dec 27, 2010 4:14 am

If you really have a 25% probability, then yes, one would expect on average 4 applications to yield about 1 acceptance. But as has been said, it is far from guaranteed...there's a chance it could yield no acceptances.

Now...if some admissions calculator or something says you have a 25% probability of admission, this doesn't really mean that YOU have a 25% chance of admission. It means you have a 25% probability of admission given what it knows about you (numbers and URM status), and assuming that its methodology is correct.

So for example, if you have nothing beyond your numbers and only 25% of people with your numbers get in, then your probability of admission is really probably closer to 0%. At that point something like ED might put you over the top.

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Re: Admissions Probability ?

Postby Grizz » Mon Dec 27, 2010 4:14 am

If you mean you're at the 25th%tile GPA and LSAT for four schools, it's not a 25% chance, it's close to a 0% chance, and you will probably get into none of them. Medians bro.

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Re: Admissions Probability ?

Postby Ragged » Mon Dec 27, 2010 4:15 am

Pneumatic wrote:
nullisecundus wrote:Besides, admission to each school is an independent event, as in, your admission or rejection any one of them does not affect your chance of admission for other schools. Thus, adding the probabilities together is just dumb. Its like saying, there is a 50 percent probability of heads in any coin toss, ergo, if I toss a coin 2 times, I will definitely get a heads result.


You should statistically get heads at least once if you flip a coin twice. Wow...


Dude...

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Nulli Secundus
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Re: Admissions Probability ?

Postby Nulli Secundus » Mon Dec 27, 2010 4:15 am

Pneumatic wrote:
nullisecundus wrote:Besides, admission to each school is an independent event, as in, your admission or rejection any one of them does not affect your chance of admission for other schools. Thus, adding the probabilities together is just dumb. Its like saying, there is a 50 percent probability of heads in any coin toss, ergo, if I toss a coin 2 times, I will definitely get a heads result.


You should statistically get heads at least once if you flip a coin twice. Wow...


I think you need to check word "definitely" in the dictionary.

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Re: Admissions Probability ?

Postby Pneumatic » Mon Dec 27, 2010 4:16 am

Ragged wrote:
Pneumatic wrote:All things being equal (softs, etc.), if a person applied to 4 different schools, each of which, statistically, he had a 25% probability of being accepted at, is it likely (statistically) he would get accepted to at least one of those schools? It appears to me that probability theory suggests he should; however, it also kind of seems unlikely. Does normal statistical theory apply to Law admissions as represented in this post, or would it differ in some way for some reason?


I sorta doubte that. Even if you could know what your exact probability is (which you can't), I'm pretty sure that's not how these things work.


I agree with you. I think. But, why doesn't these things work within normal probability, if they don't is the real question.

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Re: Admissions Probability ?

Postby 09042014 » Mon Dec 27, 2010 4:18 am

Pneumatic wrote:
Ragged wrote:
Pneumatic wrote:All things being equal (softs, etc.), if a person applied to 4 different schools, each of which, statistically, he had a 25% probability of being accepted at, is it likely (statistically) he would get accepted to at least one of those schools? It appears to me that probability theory suggests he should; however, it also kind of seems unlikely. Does normal statistical theory apply to Law admissions as represented in this post, or would it differ in some way for some reason?


I sorta doubte that. Even if you could know what your exact probability is (which you can't), I'm pretty sure that's not how these things work.


I agree with you. I think. But, why doesn't these things work within normal probability, if they don't is the real question.


Because they aren't random processes.

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Re: Admissions Probability ?

Postby Nulli Secundus » Mon Dec 27, 2010 4:20 am

Desert Fox wrote:
Pneumatic wrote:
Ragged wrote:
Pneumatic wrote:All things being equal (softs, etc.), if a person applied to 4 different schools, each of which, statistically, he had a 25% probability of being accepted at, is it likely (statistically) he would get accepted to at least one of those schools? It appears to me that probability theory suggests he should; however, it also kind of seems unlikely. Does normal statistical theory apply to Law admissions as represented in this post, or would it differ in some way for some reason?


I sorta doubte that. Even if you could know what your exact probability is (which you can't), I'm pretty sure that's not how these things work.


I agree with you. I think. But, why doesn't these things work within normal probability, if they don't is the real question.


Because they aren't random processes.


This is our assumption though. Maybe ad-comms use the "staircase grading" method for borderline cases, although even then, if they use the "toss down the stairs and admit the farthest" method, the addenda and LOCIs weighing down your file may decrease your chances. Depends on the method :P

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Re: Admissions Probability ?

Postby WhatSarahSaid » Mon Dec 27, 2010 4:26 am

Solution: Apply to the schools this year. If you get shut out, just apply to all of them next year. Since you got shut out, your chances of getting in will go up next year.

I'm a gambler, so I don't commit fallacies.

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Re: Admissions Probability ?

Postby 09042014 » Mon Dec 27, 2010 4:27 am

nullisecundus wrote:
This is our assumption though. Maybe ad-comms use the "staircase grading" method for borderline cases, although even then, if they use the "toss down the stairs and admit the farthest" method, the addenda and LOCIs weighing down your file may decrease your chances. Depends on the method :P


Then they aren't independent events like you said with softs and the like.

If you further assume they are independent events, then it would follow probability theory. The probability of 4 chances at 25% a piece getting an acceptance at least 1 times is ~68%. You multiple probabilities to find the probability they all happen (if they are all independent).

The short cut is finding the probablity that you get zero out of four. (.75)^4= .316

Then you subtract that from 1 to find the probabilty of every other permutation and you get .684 or 68.4%

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Re: Admissions Probability ?

Postby Ragged » Mon Dec 27, 2010 4:33 am

Pneumatic wrote:
Ragged wrote:
Pneumatic wrote:All things being equal (softs, etc.), if a person applied to 4 different schools, each of which, statistically, he had a 25% probability of being accepted at, is it likely (statistically) he would get accepted to at least one of those schools? It appears to me that probability theory suggests he should; however, it also kind of seems unlikely. Does normal statistical theory apply to Law admissions as represented in this post, or would it differ in some way for some reason?


I sorta doubte that. Even if you could know what your exact probability is (which you can't), I'm pretty sure that's not how these things work.


I agree with you. I think. But, why doesn't these things work within normal probability, if they don't is the real question.


My statistics is really fuzzy but I'm sure someone will correct me if the following is completly wrong.

Let's say there is a 4 sided die and we are trying to roll a 1. We have 4 tosses. Probability of not rolling a 1 is .75. What's the probability of not getting a 1 for all four rolls. It's .75*.75*.75*.75 = .3164 Which means that you have ~70 (1-.3164) of rolling a 1 atleast once in the four rolls.

So yea, if it was completely random and the events were completely independent than you would have an OK, but not still not great, chance of being admitted.

[EDIT] DF beat me to it.


The problem here is that there is no way to know what your chances really are, because we don't know the number of applicants, the number of spots, ad comm's goals, what they might like about your app besides your stats.

LSP is not going to help with this either. 25% on there on is more like 0 for most purposes.

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Re: Admissions Probability ?

Postby tgir » Mon Dec 27, 2010 4:39 am

Normal statistical theory does apply to the extent that you can actually estimate your admissions probabilities from past data--which isn't a terribly great extent in the case of law school admissions, in my opinion. Still, though, the calculation you described is too simplistic.

You're partially correct, in that the probability of one of many outcomes occurring is related to the sum of the probabilities of each of those outcomes. But there's a critical component missing: the overlap in the probabilities, which you must subtract from the sum of the separate probabilities. Think about it: if you upped the number of law schools to 5, would the person now have a 125% chance of getting into one of them? Obviously not.

So, in this case, you would add up 25+25+25+25, but you would also have to subtract portions for the probabilities that more than one of the schools would accept the student. In law school admissions, these overlaps tend to be high. So while School A might give you a 50% chance and School B might also give you a 50% chance, if the probability of BOTH School A and School B letting you in is 30%, then you've got (50+50)-30=70% chance at getting into one of them--not a 100% chance.

Another way to think of this is as follows: if two schools have the same criteria for admissions, applying to the second one isn't going to suddenly cover more ground than would be covered by the first--the probability "potential" left uncovered by A is also not covered by B. You'd be better off applying to another school with completely different admissions criteria, assuming you had a good shot under both systems.

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Bildungsroman
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Re: Admissions Probability ?

Postby Bildungsroman » Mon Dec 27, 2010 4:43 am

This is silly. You never have a % chance of admission because there is no random element to the process. Either you meet the criteria of the admissions committee or you do not. Granted, there can be a lot of variable at play depending on the school (date of submission, C+F responses, etc) but an admissions committee never puts all the applications in a bingo hopper and then pulls them out at random to decide acceptances.

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Re: Admissions Probability ?

Postby Pneumatic » Mon Dec 27, 2010 4:46 am

tgir wrote:Normal statistical theory does apply to the extent that you can actually estimate your admissions probabilities from past data--which isn't a terribly great extent in the case of law school admissions, in my opinion. Still, though, the calculation you described is too simplistic.

You're partially correct, in that the probability of one of many outcomes occurring is related to the sum of the probabilities of each of those outcomes. But there's a critical component missing: the overlap in the probabilities, which you must subtract from the sum of the separate probabilities. Think about it: if you upped the number of law schools to 5, would the person now have a 125% chance of getting into one of them? Obviously not.

So, in this case, you would add up 25+25+25+25, but you would also have to subtract portions for the probabilities that more than one of the schools would accept the student. In law school admissions, these overlaps tend to be high. So while School A might give you a 50% chance and School B might also give you a 50% chance, if the probability of BOTH School A and School B letting you in is 30%, then you've got (50+50)-30=70% chance at getting into one of them--not a 100% chance.

Another way to think of this is as follows: if two schools have the same criteria for admissions, applying to the second one isn't going to suddenly cover more ground than would be covered by the first--the probability "potential" left uncovered by A is also not covered by B. You'd be better off applying to another school with completely different admissions criteria, assuming you had a good shot under both systems.


Thanks. Great analysis. I was just curious what the answers would be on this forum.

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Re: Admissions Probability ?

Postby 09042014 » Mon Dec 27, 2010 4:48 am

Pneumatic wrote:
tgir wrote:Normal statistical theory does apply to the extent that you can actually estimate your admissions probabilities from past data--which isn't a terribly great extent in the case of law school admissions, in my opinion. Still, though, the calculation you described is too simplistic.

You're partially correct, in that the probability of one of many outcomes occurring is related to the sum of the probabilities of each of those outcomes. But there's a critical component missing: the overlap in the probabilities, which you must subtract from the sum of the separate probabilities. Think about it: if you upped the number of law schools to 5, would the person now have a 125% chance of getting into one of them? Obviously not.

So, in this case, you would add up 25+25+25+25, but you would also have to subtract portions for the probabilities that more than one of the schools would accept the student. In law school admissions, these overlaps tend to be high. So while School A might give you a 50% chance and School B might also give you a 50% chance, if the probability of BOTH School A and School B letting you in is 30%, then you've got (50+50)-30=70% chance at getting into one of them--not a 100% chance.

Another way to think of this is as follows: if two schools have the same criteria for admissions, applying to the second one isn't going to suddenly cover more ground than would be covered by the first--the probability "potential" left uncovered by A is also not covered by B. You'd be better off applying to another school with completely different admissions criteria, assuming you had a good shot under both systems.


Thanks. Great analysis. I was just curious what the answers would be on this forum.



This guy doesn't know what the fuck he is talking about and cannot do basic probability.

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tgir
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Re: Admissions Probability ?

Postby tgir » Mon Dec 27, 2010 4:50 am

Desert Fox wrote:
Pneumatic wrote:
tgir wrote:Normal statistical theory does apply to the extent that you can actually estimate your admissions probabilities from past data--which isn't a terribly great extent in the case of law school admissions, in my opinion. Still, though, the calculation you described is too simplistic.

You're partially correct, in that the probability of one of many outcomes occurring is related to the sum of the probabilities of each of those outcomes. But there's a critical component missing: the overlap in the probabilities, which you must subtract from the sum of the separate probabilities. Think about it: if you upped the number of law schools to 5, would the person now have a 125% chance of getting into one of them? Obviously not.

So, in this case, you would add up 25+25+25+25, but you would also have to subtract portions for the probabilities that more than one of the schools would accept the student. In law school admissions, these overlaps tend to be high. So while School A might give you a 50% chance and School B might also give you a 50% chance, if the probability of BOTH School A and School B letting you in is 30%, then you've got (50+50)-30=70% chance at getting into one of them--not a 100% chance.

Another way to think of this is as follows: if two schools have the same criteria for admissions, applying to the second one isn't going to suddenly cover more ground than would be covered by the first--the probability "potential" left uncovered by A is also not covered by B. You'd be better off applying to another school with completely different admissions criteria, assuming you had a good shot under both systems.


Thanks. Great analysis. I was just curious what the answers would be on this forum.



This guy doesn't know what the fuck he is talking about and cannot do basic probability.


Ouch. Someone has a lot of anger. Feel free to point out the errors, but please don't be an asshole.

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Re: Admissions Probability ?

Postby Pneumatic » Mon Dec 27, 2010 4:51 am

Desert Fox wrote:
Pneumatic wrote:
tgir wrote:Normal statistical theory does apply to the extent that you can actually estimate your admissions probabilities from past data--which isn't a terribly great extent in the case of law school admissions, in my opinion. Still, though, the calculation you described is too simplistic.

You're partially correct, in that the probability of one of many outcomes occurring is related to the sum of the probabilities of each of those outcomes. But there's a critical component missing: the overlap in the probabilities, which you must subtract from the sum of the separate probabilities. Think about it: if you upped the number of law schools to 5, would the person now have a 125% chance of getting into one of them? Obviously not.

So, in this case, you would add up 25+25+25+25, but you would also have to subtract portions for the probabilities that more than one of the schools would accept the student. In law school admissions, these overlaps tend to be high. So while School A might give you a 50% chance and School B might also give you a 50% chance, if the probability of BOTH School A and School B letting you in is 30%, then you've got (50+50)-30=70% chance at getting into one of them--not a 100% chance.

Another way to think of this is as follows: if two schools have the same criteria for admissions, applying to the second one isn't going to suddenly cover more ground than would be covered by the first--the probability "potential" left uncovered by A is also not covered by B. You'd be better off applying to another school with completely different admissions criteria, assuming you had a good shot under both systems.


Thanks. Great analysis. I was just curious what the answers would be on this forum.



This guy doesn't know what the fuck he is talking about and cannot do basic probability.


Maybe, maybe be not, but it sounds good and appears to be right, probably.

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Re: Admissions Probability ?

Postby 09042014 » Mon Dec 27, 2010 4:52 am

tgir wrote:
Ouch. Someone has a lot of anger. Feel free to point out the errors, but please don't be an asshole.


You don't understand basic probability at even a 5th grade level.

You don't add the probability of independent events you multiply.

09042014
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Re: Admissions Probability ?

Postby 09042014 » Mon Dec 27, 2010 4:53 am

Pneumatic wrote:
Maybe, maybe be not, but it sounds good and appears to be right, probably.


Well it isn't.

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tgir
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Re: Admissions Probability ?

Postby tgir » Mon Dec 27, 2010 4:54 am

Desert Fox wrote:
tgir wrote:
Ouch. Someone has a lot of anger. Feel free to point out the errors, but please don't be an asshole.


You don't understand basic probability at even a 5th grade level.

You don't add the probability of independent events you multiply.


That depends on whether you're talking about the union or the intersection. OP was asking about the union, I believe.




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