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[quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous]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!!![/quote]

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.[/quote] 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.[/quote]

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.[/quote]

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[/quote]

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

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

You need to do better at this.  This is awful.[/quote] 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.[/quote]

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.[/quote] 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)[/quote]

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