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Math Help - Question on Probability!

  1. #1
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    Question on Probability!

    49. On a multiple choice test of 10 questions, each question has 5 possible answers. A student is certain of the answers to 4 questions but is totally baffled by 6 questions. If the student randomly guesses the answer to those 6 questions, what is the probability that the student will get a score of 5 or more on the test? Express your answer correct to two decimal places. out of 4 marks
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    Quote Originally Posted by cnmath16 View Post
    49. On a multiple choice test of 10 questions, each question has 5 possible answers. A student is certain of the answers to 4 questions but is totally baffled by 6 questions. If the student randomly guesses the answer to those 6 questions, what is the probability that the student will get a score of 5 or more on the test? Express your answer correct to two decimal places. out of 4 marks
    Since the student is certain to get at least 4 of the questions correct, he is getting at least a 4 on the exam, then. Thus, it is equivalent to having a 6 (10 questions - 4 guarantees) question test and asking about the probability of getting 1 or more on the exam.

    We observe that the chances of him getting any one question correct is 1/5, or 20% and of course, the chance of him getting it wrong would be 4/5, or 80%. Find the probability that he gets all 6 questions wrong first. By independent, we can simply multiple and get 0.8^6. So that chance that he gets at least 1 question right is the complement of the previous probability, or 1-0.8^6.
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