Simple probability does not begin to touch the algorithms involved in modern college admissions via the enrollment management industry. Probability is just not how it works.

This is silly. The question is the likelihood of at least one acceptance among students who apply to the same 10 schools each with a 4% acceptance rate. The answer will be between 4% and 33% (OP's math). But there's nothing to narrow it down within that range. The upper bound happens when the acceptances distribute randomly across the 10 schools (the schools may as well be pulling names from a hat), the lower bound happens when all choose the same subset of students (the schools are all using the same algorithm). All an individual student can know is their personal odds are not worse if they apply to more schools. But they already knew that.

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

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Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:They are not totally independent, but also not totally dependent. But your point is taken.

The takeaway is that college admission is NOT a lottery system like some posters claimed.

If your stats puts on in the game, you want to apply to AS MANY top 20 as possible!!!

In mathematical terms, related to game theory, they are totally independent events, in that the outcome of one does not affect the outcome of another.

https://mathematicalmysteries.org/independent-and-dependent-events/

But as noted, despite that you cannot use game theory because you can’t know the starting odds of your admission the way you can know that you have a 1 in 52 chance of drawing the 8 of hearts from a full deck of cards.

The occurrence of one does affect the probability of the others also occurring. If a student is in at MIT and Harvard, there is a greater than 4% chance of them also being in at Princeton.

What was the student’s odds at Princeton before they were accepted to MIT and Harvard? How did they change AFTER acceptance to MIT and Harvard? (They didn’t).

That is what dependent events are - that change the likelihood. If the likelihood does NOT change, they are independent events. Game Theory requires independent events for the formula shown to work.

You are speaking about correlation. https://en.m.wikipedia.org/wiki/Correlation.

Do not use game theory when developing a college application strategy.

Correlation is a type of dependence. Two events that are correlated can not be independent.

https://stats.stackexchange.com/questions/509141/correlation-vs-dependence-vs-causality/509221#509221

Your own link is entitled correlation-vs-dependence-vs-causality. vs stands for VERSUS. Meaning they are different.

More importantly, this article has nothing to do with dependent events and independent events in probability. A link explaining that was posted above. You choose to ignore it.

You need to do better at this. This is awful.

Of course they are different. Correlation is a particular type of dependence. Correlation implies dependence, not the other way around. Hence, they're different, even though one is a type of the other. Learn basic logic before learning probability, please. A little knowledge is a dangerous thing and all that.

No you are completely wrong. This topic is about probability and dependent and independent events are very specific. Correlation has nothing to do with it.

In the future I recommend you not insult others when you are the wrong one.

Ironic given that you have a much more aggressive tone than me despite not understandingnthe relationship between correlation and dependence.

Also, I didn't bring correlation into this, I just said they were dependent (which they are), and you (or someone else) said I was speaking about correlation as if the two were mutually exclusive, when in fact one is a special case of the other. (See the CMU handout for details that are actually specific and relevant)

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:They are not totally independent, but also not totally dependent. But your point is taken.

The takeaway is that college admission is NOT a lottery system like some posters claimed.

If your stats puts on in the game, you want to apply to AS MANY top 20 as possible!!!

In mathematical terms, related to game theory, they are totally independent events, in that the outcome of one does not affect the outcome of another.

https://mathematicalmysteries.org/independent-and-dependent-events/

But as noted, despite that you cannot use game theory because you can’t know the starting odds of your admission the way you can know that you have a 1 in 52 chance of drawing the 8 of hearts from a full deck of cards.

The occurrence of one does affect the probability of the others also occurring. If a student is in at MIT and Harvard, there is a greater than 4% chance of them also being in at Princeton.

What was the student’s odds at Princeton before they were accepted to MIT and Harvard? How did they change AFTER acceptance to MIT and Harvard? (They didn’t).

That is what dependent events are - that change the likelihood. If the likelihood does NOT change, they are independent events. Game Theory requires independent events for the formula shown to work.

You are speaking about correlation. https://en.m.wikipedia.org/wiki/Correlation.

Do not use game theory when developing a college application strategy.

Correlation is a type of dependence. Two events that are correlated can not be independent.

https://stats.stackexchange.com/questions/509141/correlation-vs-dependence-vs-causality/509221#509221

Your own link is entitled correlation-vs-dependence-vs-causality. vs stands for VERSUS. Meaning they are different.

More importantly, this article has nothing to do with dependent events and independent events in probability. A link explaining that was posted above. You choose to ignore it.

You need to do better at this. This is awful.

Of course they are different. Correlation is a particular type of dependence. Correlation implies dependence, not the other way around. Hence, they're different, even though one is a type of the other. Learn basic logic before learning probability, please. A little knowledge is a dangerous thing and all that.

No you are completely wrong. This topic is about probability and dependent and independent events are very specific. Correlation has nothing to do with it.

In the future I recommend you not insult others when you are the wrong one.

Did you not read this? Was the math too scary?

https://www.stat.cmu.edu/~cshalizi/uADA/13/reminders/uncorrelated-vs-independent.pdf

Anonymous wrote:

Anonymous wrote:Um, math no workey OP.

If college acceptance was like drawing names from a hat, 4% acceptance means a 1 in 25 chance. So argued, apply to 25 schools, winner chosen at random, might get into 1.

But names aren't randomly selected. The 4% chance simply means almost zero applicants meet the admission criteria

The reality is that far more applicants meet the admission criteria.

The reality is that it's very rare a single applicant sweep all top 20 schools.

The reality is that it's also very rare a single applicant who met the criteria got rejected by all top 20 schools.

The reality is that a typically applicant got waitlisted by a few and rejected by a few, but accepted by one or two.

It only 4% offered admission, 96% didn't meet criteria to get an offer, that is almost zero mathematically.

Somebody had to say it.

Anonymous wrote:Also please stop using the term game theory. This is simple high school probability, although it might be in Harvards remedial math class

I think the OP makes more sense than some claim, at least today compared to the past. When I applied to colleges it was clearly very driven by GPAs and SAT scores; while you couldn't predict what colleges you would get into, it was unusual to get accepted to a more selective college and then rejected by less selective schools.

Today, with GPA and SAT inflation, applicants are much, much more similar on the measurables. Which means it comes down to different factors. Sure, some ECs are clearly more attractive, but it also can come down to the intangibles that may appeal to one college but not appeal to others.

In those cases where factors other then GPA/SAT scores are the tie breaker, the applications are (more or less) independent events. And so it does kind of make sense to apply to more schools, at least if the application quality can be maintained.

Anonymous wrote:Assuming they are all independent separate events, the probability of receiving at least one acceptance is 33% if you apply to 10 colleges each with 4% admit rate.

Anonymous wrote:
What was the student’s odds at Princeton before they were accepted to MIT and Harvard? How did they change AFTER acceptance to MIT and Harvard? (They didn’t).

before, whatever the Princeton admit rate was

After, some larger amount as the odds of getting into P conditional on having already gotten in to M or H are greater than just the odds of getting into P. Getting into universities are correlated events and therefore dependent.