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# help

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A multiple-choice test has 6 questions. Each question has 5 choices and only one of which is correct. If a student guesses the answer for each question find the probability that the students gets exactly 3 questions correct

Mar 8, 2020

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There are 6 choose 3 or 20 total arrangements of questions.

The chance that a student gets one right is 1/5 and wrong is 4/5.

Since we want to find 3 questions correct, it is $$(\frac{1}{5})^3\times (\frac{4}{5})^3$$, or 64/15625

But we have to multiply by 20 to get 1280/15625, simplified to 256/3125.

You are very welcome!

:P

Mar 8, 2020