Solving Misprints: A Problem of Undetected Errors
Two proof-readers are checking a manuscript but find different numbers of errors. When only the errors they both find are compared, it reveals a specific pattern. This challenge prompts an exploration of the likelihood of undetected errors and how to approach similar problems by setting specific integer values. By manipulating the variables, one can control the number of errors left unnoticed, offering a unique perspective on problem-solving strategies.
Download Presentation
Please find below an Image/Link to download the presentation.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author. Download presentation by click this link. If you encounter any issues during the download, it is possible that the publisher has removed the file from their server.
E N D
Presentation Transcript
Misprints Do Hapen Source: David Wells Sunday Telegraph 18/9/16
Misprints Do Hapen Two proof-readers are checking separate copies of the same manuscript. The first finds ?? errors, and the second only ??. When their completed proofs are compared, it turns out that only ?? errors have been spotted by both of them. How many errors would you suspect remain, undetected by either of them?
Misprints Do Hapen Proof-reader ? Proof-reader ? ?? ?? ?? ?? ?
Misprints Do Hapen ?? ?? ? Let s assume there are ? errors to be found in the manuscript. The probability that ? finds an error is ?? ? , and ?, ?? ? . Since they are working independently the probability of finding the same errors is ?? ? ?? ? . The expectation of the number of joint errors found is thus ?? ? ?? ? ?, which we are told is ??.
Misprints Do Hapen ?? ?? ? ?? ? ?? ? ? = ?? ?? ? ?? = ?? ?? ?? ?? ? = ?? = ? So the number of errors we expect to be missed by both proof-readers is, on average, ?? ?? + ?? + ? = ?
Misprints Do Hapen Can you create your own version of the problem such that the number of undetected errors is ? (or any other number for that matter)? How should you set about the task? You could use trial and improvement but that wouldn t help you create multiple solutions easily. Let s look at the general case. ? ? ? ?
Misprints Do Hapen ? ? ? ? ?+? ?+? As before: ?+?+?+? ?+?+?+? ? + ? + ? + ? = ? ? + ? ? + ? = ? + ? + ? + ? ? ?? + ?? + ?? + ??= ?? + ?? + ??+ ?? ?? = ?? ? =?? ? So just choose your integer values ?, ? and ? to give the desired result.
SIC_50 Misprints Do Hapen Two proof-readers are checking separate copies of the same manuscript. The first finds ?? errors, and the second only ??. When their completed proofs are compared, it turns out that only ?? errors have been spotted by both of them. How many errors would you suspect remain, undetected by either of them?
SIC_50 Misprints Do Hapen Two proof-readers are checking separate copies of the same manuscript. The first finds ?? errors, and the second also ??. When their completed proofs are compared, it turns out that only ?? errors have been spotted by both of them. How many errors would you suspect remain, undetected by either of them?
SIC_50 Misprints Do Hapen Two proof-readers are checking separate copies of the same manuscript. The first finds ?? errors, and the second only ??. When their completed proofs are compared, it turns out that only ?? errors have been spotted by both of them. How many errors would you suspect remain, undetected by either of them?
SIC_50 Misprints Do Hapen Two proof-readers are checking separate copies of the same manuscript. The first finds ?? errors, and the second only ??. When their completed proofs are compared, it turns out that only ?? errors have been spotted by both of them. How many errors would you suspect remain, undetected by either of them?
SIC_50 Misprints Do Hapen Two proof-readers are checking separate copies of the same manuscript. The first finds ?? errors, and the second only ??. When their completed proofs are compared, it turns out that only ?? errors have been spotted by both of them. How many errors would you suspect remain, undetected by either of them?
SIC_50 Misprints Do Hapen Two proof-readers are checking separate copies of the same manuscript. The first finds ?? errors, and the second only ??. When their completed proofs are compared, it turns out that only ?? errors have been spotted by both of them. How many errors would you suspect remain, undetected by either of them?
SIC_50 Misprints Do Hapen Two proof-readers are checking separate copies of the same manuscript. The first finds ?? errors, and the second only ??. When their completed proofs are compared, it turns out that only ?? errors have been spotted by both of them. How many errors would you suspect remain, undetected by either of them?
SIC_50 Misprints Do Hapen Two proof-readers are checking separate copies of the same manuscript. The first finds ?? errors, and the second only ??. When their completed proofs are compared, it turns out that only ?? errors have been spotted by both of them. How many errors would you suspect remain, undetected by either of them?
SIC_50 Misprints Do Hapen Two proof-readers are checking separate copies of the same manuscript. The first finds ?? errors, and the second only ??. When their completed proofs are compared, it turns out that only ?? errors have been spotted by both of them. How many errors would you suspect remain, undetected by either of them?
SIC_50 Misprints Do Hapen Two proof-readers are checking separate copies of the same manuscript. The first finds ?? errors, and the second only ?. When their completed proofs are compared, it turns out that only ? errors have been spotted by both of them. How many errors would you suspect remain, undetected by either of them?
SIC_50 Misprints Do Hapen Two proof-readers are checking separate copies of the same manuscript. The first finds ? errors, and the second only ?. When their completed proofs are compared, it turns out that only ? errors have been spotted by both of them. How many errors would you suspect remain, undetected by either of them?
SIC_50 Misprints Do Hapen Two proof-readers are checking separate copies of the same manuscript. The first finds ? errors, and the second also ?. When their completed proofs are compared, it turns out that only ? errors have been spotted by both of them. How many errors would you suspect remain, undetected by either of them?
SIC_50 Misprints Do Hapen Two proof-readers are checking separate copies of the same manuscript. The first finds ?? errors, and the second also ??. When their completed proofs are compared, it turns out that only ? errors have been spotted by both of them. How many errors would you suspect remain, undetected by either of them?
SIC_50 Misprints Do Hapen Two proof-readers are checking separate copies of the same manuscript. The first finds ?? errors, and the second also ??. When their completed proofs are compared, it turns out that only ?? errors have been spotted by both of them. How many errors would you suspect remain, undetected by either of them?
SIC_50 Misprints Do Hapen Two proof-readers are checking separate copies of the same manuscript. The first finds ?? errors, and the second also ??. When their completed proofs are compared, it turns out that only ?? errors have been spotted by both of them. How many errors would you suspect remain, undetected by either of them?
SIC_50 Misprints Do Hapen Two proof-readers are checking separate copies of the same manuscript. The first finds ?? errors, and the second also ??. When their completed proofs are compared, it turns out that only ?? errors have been spotted by both of them. How many errors would you suspect remain, undetected by either of them?
