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3. Bayes' Theorem. On September 2nd Student Health sent a letter informing that in the previous week n=35,000 Covid-19 tests were performed. After double checking it was confirmed that of these, T=175 students had the virus. That is, P(T)=0.005. The test swabs used had a 98% sensitivity, that is the probability of designating an infected individual as positive, P(+|T). Also the tests has a 99% specificity, that is the probability of designating a healthy individual as negative, P(-|F). Suppose that during that week you took a single test and you resulted positive (+), what are the odds that you were a false positive? Find P(F|+) and show your work with a tree diagram.

3. Bayes' Theorem. On September 2nd Student Health sent a letter informing that in the previous week n=35,000 Covid-19 tests were performed. After double checking it was confirmed that of these, T=175 students had the virus. That is, P(T)=0.005. The test swabs used had a 98% sensitivity, that is the probability of designating an infected individual as positive, P(+|T). Also the tests has a 99% specificity, that is the probability of designating a healthy individual as negative, P(-|F). Suppose that during that week you took a single test and you resulted positive (+), what are the odds that you were a false positive? Find P(F|+) and show your work with a tree diagram.

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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3. Bayes' Theorem. On September 2nd the previous week n=35,000 Covid-19 tests were performed. After double checking it was confirmed that of these, T=175 students had the virus. That is, P(T)=0.005. The test Student Health sent a letter informing that in swabs used had a 98% sensitivity, that is the probability of designating an infected individual as positive, P(+|T). Also the tests has a 99% specificity, that is the probability of designating a healthy individual as negative, P(-|F). Suppose that during that week you took a single test and you resulted positive (+), what are the odds that you were a false positive? Find P(F|+) and show your work with a tree diagram.
Transcribed Image Text:3. Bayes' Theorem. On September 2nd the previous week n=35,000 Covid-19 tests were performed. After double checking it was confirmed that of these, T=175 students had the virus. That is, P(T)=0.005. The test Student Health sent a letter informing that in swabs used had a 98% sensitivity, that is the probability of designating an infected individual as positive, P(+|T). Also the tests has a 99% specificity, that is the probability of designating a healthy individual as negative, P(-|F). Suppose that during that week you took a single test and you resulted positive (+), what are the odds that you were a false positive? Find P(F|+) and show your work with a tree diagram.
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