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What is the probability of a student pass the following exam by guessing and getting at...

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surfer3 | Valedictorian

Posted May 25, 2012 at 3:12 AM via web

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What is the probability of a student pass the following exam by guessing and getting at least 45 correct answers?

The midterm exam in a nursing course consists of 75 t/f questions. Assume that an unprepared student makes random guesses for each of the answers.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted May 25, 2012 at 3:34 AM (Answer #1)

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The exam consists of 75 true/false questions. Each question has two answers and if a person makes a random guess the probability of getting a correct answer is equal to that of getting an incorrect answer, both the probabilities are (1/2).

If a student were to answer all the questions by making random guesses, the probability of getting at least 45 answers correct is 1 - probability of getting 44 correct answers

=> `1 - C(75, 44)*(1/2)^44*(1/2)^31`

=> `1 - 0.030`

`~~ 0.9699`

The probability of the student getting at least 45 right answers is 0.9699.

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