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6. (a) Suppose an at-home test is 99 percent effective at detecting a disease when the person has the disease. However, the test also has a "false positive" rate, as 1 percent of people who do not have the disease who are tested get a positive result. Suppose 0.5 percent of the population has the disease. What is the probability that a person has the disease, given that they get a positive result on this test? (Hint: use what you did in the previous problem.) (b) Suppose now that only .05 percent of the population has the disease. What is the probability that a person has the disease, given that they get a positive result on this test? (c) Think about what you've just calculated. Do you find this surprising? Briefly ex- plain. (For your general knowledge, the calculation you've done in this problem is an application of what's called Bayes' formula. It is very important in probability and statistics, and can lead to results that people find very non-intuitive.)

6. (a) Suppose an at-home test is 99 percent effective at detecting a disease when the person has the disease. However, the test also has a "false positive" rate, as 1 percent of people who do not have the disease who are tested get a positive result. Suppose 0.5 percent of the population has the disease. What is the probability that a person has the disease, given that they get a positive result on this test? (Hint: use what you did in the previous problem.) (b) Suppose now that only .05 percent of the population has the disease. What is the probability that a person has the disease, given that they get a positive result on this test? (c) Think about what you've just calculated. Do you find this surprising? Briefly ex- plain. (For your general knowledge, the calculation you've done in this problem is an application of what's called Bayes' formula. It is very important in probability and statistics, and can lead to results that people find very non-intuitive.)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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No 6. a, b, c, pls 

D Read aloud + 3 of 5 5 6. (a) Suppose an at-home test is 99 percent effective at detecting a disease when the person has the disease. However, the test also has a "false positive" rate, as 1 percent of people who do not have the disease who are tested get a positive result. Suppose 0.5 percent of the population has the disease. What is the probability that a person has the disease, given that they get a positive result on this test? (Hint: use what you did in the previous problem.) (b) Suppose now that only .05 percent of the population has the disease. What is the probability that a person has the disease, given that they get a positive result on this test? (c) Think about what you've just calculated. Do you find this surprising? Briefly ex- plain. (For your general knowledge, the calculation you've done in this problem is an application of what's called Bayes' formula. It is very important in probability and statistics, and can lead to results that people find very non-intuitive.) 7. (a) In the figure below, find a transition matrix for the Markov model labeled Model 1. (b) What does the number 0.3 on the top arrow represent? Be precise. (c) What happens to your transition matrix if you make a different choice for how to label the states? Briefly explain.
Transcribed Image Text:D Read aloud + 3 of 5 5 6. (a) Suppose an at-home test is 99 percent effective at detecting a disease when the person has the disease. However, the test also has a "false positive" rate, as 1 percent of people who do not have the disease who are tested get a positive result. Suppose 0.5 percent of the population has the disease. What is the probability that a person has the disease, given that they get a positive result on this test? (Hint: use what you did in the previous problem.) (b) Suppose now that only .05 percent of the population has the disease. What is the probability that a person has the disease, given that they get a positive result on this test? (c) Think about what you've just calculated. Do you find this surprising? Briefly ex- plain. (For your general knowledge, the calculation you've done in this problem is an application of what's called Bayes' formula. It is very important in probability and statistics, and can lead to results that people find very non-intuitive.) 7. (a) In the figure below, find a transition matrix for the Markov model labeled Model 1. (b) What does the number 0.3 on the top arrow represent? Be precise. (c) What happens to your transition matrix if you make a different choice for how to label the states? Briefly explain.
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