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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!

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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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.

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