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(a) A multiple-choice test paper contains 50 questions; for each question three answers are given, one of which is correct. The two incorrect answers to any question are designed to be plausible, so that an ignorant candidate could be expected to pick an answer quite at random. If the examination is marked simply by giving one mark per correct answer, what should the pass mark be if the probability that a completely ignorant candidate passes is to be approximately 1%?

(a) A multiple-choice test paper contains 50 questions; for each question three answers are given, one of which is correct. The two incorrect answers to any question are designed to be plausible, so that an ignorant candidate could be expected to pick an answer quite at random. If the examination is marked simply by giving one mark per correct answer, what should the pass mark be if the probability that a completely ignorant candidate passes is to be approximately 1%?

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section11.8: Probabilities Of Disjoint And Overlapping Events
Problem 2C
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(a) A multiple-choice test paper contains 50 questions; for each question three answers are given, one of which is correct. The two incorrect answers to any question are designed to be plausible, so that an ignorant candidate could be expected to pick an answer quite at random. If the examination is marked simply by giving one mark per correct answer, what should the pass mark be if the probability that a completely ignorant candidate passes is to be approximately 1%? (b) Suppose now that the examination is marked by awarding two marks per correct answer, but deducting one mark for every incorrect answer. If an ignorant candidate attempts every question, what is the expectation and variance of the candidate's total score? (c) Consider the position of a candidate when the scoring system is as in part (b), but with only one mark for a correct answer, and when the pass mark is 28. The candidate has revised half the syllabus thoroughly, and finds that he is certain of the correct answers to half the questions. To gain the extra 3 marks needed to pass he decides to guess at the answers to a few more questions. Would the probability of passing be greater if he picked just three more questions hoping to get them all correct, or if he guessed at five questions?
Transcribed Image Text:(a) A multiple-choice test paper contains 50 questions; for each question three answers are given, one of which is correct. The two incorrect answers to any question are designed to be plausible, so that an ignorant candidate could be expected to pick an answer quite at random. If the examination is marked simply by giving one mark per correct answer, what should the pass mark be if the probability that a completely ignorant candidate passes is to be approximately 1%? (b) Suppose now that the examination is marked by awarding two marks per correct answer, but deducting one mark for every incorrect answer. If an ignorant candidate attempts every question, what is the expectation and variance of the candidate's total score? (c) Consider the position of a candidate when the scoring system is as in part (b), but with only one mark for a correct answer, and when the pass mark is 28. The candidate has revised half the syllabus thoroughly, and finds that he is certain of the correct answers to half the questions. To gain the extra 3 marks needed to pass he decides to guess at the answers to a few more questions. Would the probability of passing be greater if he picked just three more questions hoping to get them all correct, or if he guessed at five questions?
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