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Probability
(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?

(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?

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Statistics and probability
(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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