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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 human 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(-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.

2. (Updating and learning biases): (a) One day, you're feeling a little under the weather. Since you're a responsible human 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(-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.

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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2. (Updating and learning biases): (a) One day, you're feeling a little under the weather. Since you're a responsible human 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(-|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.
Transcribed Image Text:2. (Updating and learning biases): (a) One day, you're feeling a little under the weather. Since you're a responsible human 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(-|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.
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