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Probability & Statistics/Getting into college

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Question
Dear Clyde,

I have applied to 4 colleges and I want to know what the probability is I get into at least one of them.  I have assumed my chances are as follows:

School 1:  5%
School 2: 15%
School 3: 15%
School 4: 30%

Thanks for your help!

Answer
It is easier to decide the probability of an exact number, like "What is the probability I get into all of them?" or "..none of them?" or even ".. exactly two of them?"

The best way to rephrase this is:

"What is the probability I get into at least one of them?"

changed into:

"What is the probability I don't get rejected from all of them?"

The probabilities of rejection are the opposite, so:

School 1: 95%
School 2: 85%
School 3: 85%
School 4: 70%

Thus the probability of getting rejected from all of them is:

0.95 0.85 0.85 0.7 = 0.4804625

So roughly 48% that you get rejected from all, thus about 52% that you get into at least one.

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Clyde Oliver

Expertise

I can answer all questions up to, and including, graduate level mathematics. I do not have expertise in statistics (I can answer questions about the mathematical foundations of statistics). I am very much proficient in probability. I am not inclined to answer questions that appear to be homework, nor questions that are not meaningful or advanced in any way.

Experience

I am a PhD educated mathematician working in research at a major university.

Organizations
AMS

Publications
Various research journals of mathematics. Various talks & presentations (some short, some long), about either interesting classical material or about research work.

Education/Credentials
BA mathematics & physics, PhD mathematics from a top 20 US school.

Awards and Honors
Various honors related to grades, various fellowships & scholarships, awards for contributions to mathematics and education at my schools, etc.

Past/Present Clients
In the past, and as my career progresses, I have worked and continue to work as an educator and mentor to students of varying age levels, skill levels, and educational levels.

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