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kdenly remember that you were a smart cookie and got vaccinated against several months ago! That means that the probability that you have when you're feeling sick (before getting tested) is a mere 20%. Given d your negative test result, what is the probability that you do, in fact, DVID? ommate, Joe, has fallen down the YouTube rabbit hole. When you tell out the situation with the test he says" "Vaccine, schmaccine! The only at matters for knowing whether you have COVID is what the test says." ognitive bias is Joe exhibiting? Use the odds form of Bayes' rule to express her roommate, Ann, is also a conspiracy theorist. When you tell her COVID in

kdenly remember that you were a smart cookie and got vaccinated against several months ago! That means that the probability that you have when you're feeling sick (before getting tested) is a mere 20%. Given d your negative test result, what is the probability that you do, in fact, DVID? ommate, Joe, has fallen down the YouTube rabbit hole. When you tell out the situation with the test he says" "Vaccine, schmaccine! The only at matters for knowing whether you have COVID is what the test says." ognitive bias is Joe exhibiting? Use the odds form of Bayes' rule to express her roommate, Ann, is also a conspiracy theorist. When you tell her COVID in

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
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2. (Updating and learning biases): (a) One day, you're feeling a little under the weather. Since you're a responsible Iuman being, you go get tested for COVID. You want to go to a party that night, so you take a rapid test. You know that the rapid test has 80% sensitivity |P(+infected) = 0.8] and a 60% specificity [P(-not infected) = 0.6). You also know that about 50% of the people in your area who feel sick have COVID. The test comes back negative. Given this, what is the probability that you do, in fact, have COVID? (b) Has this test come back positive, what would have been the probability that you do, in fact, have COVID? 1 (c) You suddenly remember that you were a smart cookie and got vaccinated against COVID several months ago! That means that the probability that you have COVID when you're feeling sick (before getting tested) is a mere 20%. Given this, and your negative test result, what is the probability that you do, in fact, have COVID? (d) Your roommate, Joe, has fallen down the YouTube rabbit hole. When you tell him about the situation with the test he says" "Vaccine, schmaccine! The only thing that matters for knowing whether you have COVID is what the test says." What cognitive bias is Joe exhibiting? Use the odds form of Bayes' rule to express the bias. (e) Your other roommate, Ann, is also a conspiracy theorist. When you tell her what's happening she says: "T'm pretty sure COVID is a hoax. Your test results are meaningless." What cognitive bias is Ann exhibiting? Use the odds form of Bayes' rule to express the bias. (f) Your mind reeling from these confusing interactions, you decide to get a second COVID test, just to make sure. To your dismay, the second test comes back positive! Given this, and the previous information you have (up to part C), what is the probability that you do, in fact, have COVID? (g) Imagine bringing the second test result back to your roommates. Would you expect Joe and Ann, when they form beliefs about the whether you're infected, to put more, less, or the same weight on the second test result as they now put on on the first test result? Use the odds form of Bayes' rule to formally show your answer.
Transcribed Image Text:2. (Updating and learning biases): (a) One day, you're feeling a little under the weather. Since you're a responsible Iuman being, you go get tested for COVID. You want to go to a party that night, so you take a rapid test. You know that the rapid test has 80% sensitivity |P(+infected) = 0.8] and a 60% specificity [P(-not infected) = 0.6). You also know that about 50% of the people in your area who feel sick have COVID. The test comes back negative. Given this, what is the probability that you do, in fact, have COVID? (b) Has this test come back positive, what would have been the probability that you do, in fact, have COVID? 1 (c) You suddenly remember that you were a smart cookie and got vaccinated against COVID several months ago! That means that the probability that you have COVID when you're feeling sick (before getting tested) is a mere 20%. Given this, and your negative test result, what is the probability that you do, in fact, have COVID? (d) Your roommate, Joe, has fallen down the YouTube rabbit hole. When you tell him about the situation with the test he says" "Vaccine, schmaccine! The only thing that matters for knowing whether you have COVID is what the test says." What cognitive bias is Joe exhibiting? Use the odds form of Bayes' rule to express the bias. (e) Your other roommate, Ann, is also a conspiracy theorist. When you tell her what's happening she says: "T'm pretty sure COVID is a hoax. Your test results are meaningless." What cognitive bias is Ann exhibiting? Use the odds form of Bayes' rule to express the bias. (f) Your mind reeling from these confusing interactions, you decide to get a second COVID test, just to make sure. To your dismay, the second test comes back positive! Given this, and the previous information you have (up to part C), what is the probability that you do, in fact, have COVID? (g) Imagine bringing the second test result back to your roommates. Would you expect Joe and Ann, when they form beliefs about the whether you're infected, to put more, less, or the same weight on the second test result as they now put on on the first test result? Use the odds form of Bayes' rule to formally show your answer.
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