Reply to Assuming they are all independent separate events, the probability of receiving at least one acceptance is 33% if you ap

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[quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous][quote=Anonymous]Two or three of you in this topic understand both the math and social science aspects of probability estimates. If you guys had usernames, I'd single you out.[/quote]

This one (04/06/2025 06:00) correctly highlighted the difference between dependent and independent events. But I have not seen anyone point out the fact that game theory cannot work because the people in the selection pool do not have equal chances of being selected.

Applications are read and the selection of any candidate for any particular school is a curated event. Selection is deterministic based on the reading of an application; [b]it is not random[/b]. Game theory does not work in this instance.[/quote]

Yes, I feel like this is what OP is missing. OP’s math only works if admissions are all random lotteries of applicants. [/quote]

Every time this board had a high stats kid rejected from all t20, every one jumped out to say, oh but college admission is a lottery!

Is it? Is it not?  Feels like catch 22.

[/quote]compare to getting into a car crash. A car crash is simply physics of one car hitting another for whatever reason. You don't have someone pulling numbers out of a hat. But you can model the probability and insurance companies do it all the time.[/quote]

Yes, they do it all the time, for a large group of people, not just for one person. College applicants are one person.   Why is this so hard to understand?

Do you think every applicant with the stats for Harvard has the same 4% chance of admission?[/quote]Do you realize how low of chance 4% already is? It is the same as having 1 thru 25 numbered balls in a binding and picking the right one on the first try. Very hard. [/quote]

No no no no no no no.

You have essentially said that every applicant has the same chance of admission.

They don’t.  And no applicant knows the difference.  Certainly not enough to use a probability formula to develop an application strategy.

It is not the same as picking a number from a finite set.  You have no idea how many balls are in the jar, so you don’t know what the odds are of you picking the right one.  It’s a useless number with no practical application.  [/quote]no one is trying to determine an actual probability , to calculate insurance premiums or whatever

It is enough to point out

1) they are independent events
2) there is enough randomness
3) that only one acceptance is sufficient

[/quote]

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