How lucky was I?

Algots

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Mar 11, 2015
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Hi!
A year ago now I applied to a university where I had to do a math test before to get in. I had to answer 24 questions and all of them had three options, a, b or c. To get in I had to get at least 12 questions right. I guessed all of the questions and handed it in. A few days later I got a letter saying that I had a place at the course. Now I'm trying to figure out what my probability of getting in to the course by guessing all the questions actually was. But I could use some help, thank you for answering!

(The story has been manipulated to make the question clearer.)
 
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