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A multiple choice test contains 12 questions each offering 4 answers, only one of which...

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nerdygirl-1996 | Student, Undergraduate | Honors

Posted July 4, 2013 at 3:27 PM via web

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A multiple choice test contains 12 questions each offering 4 answers, only one of which is correct each time. A student knows the correct asnwer to 7 of the questions  but randomly guesses the anwers to the remaining five. What is the probability  the student will get at least 10 of the twelve correct.

Tagged with binomial, math, probability

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted July 4, 2013 at 4:42 PM (Answer #2)

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There are 4 answers for each multiple choice question and each of them has only one correct answer. If any answer is chosen at random the probability of it being correct is 1/4. The probability that it is incorrect is 3/4.

In the 12 question test, the student knows the correct answer to 7 of the questions. For the other 5 questions the answers are picked at random. To get at least 10 answers right, the student should get either 3 or 4 or 5 answers correct for the 5 questions she does not know the answer to.

The probability of this is `(1/4)^3*(3/4)^2` + `(1/4)^4*(3/4)` + `(1/4)^5` = `13/1024`

The required probability is `13/1024`

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