Polymerase chain reaction (PCR) is a method widely used to diagnose COVID-19 infections. Suppose that if a person does not have COVID-19, the test will be negative 84% of the time, and be positive 16% of the time; if the person does have COVID-19, the test will be positive 88% of the time, and be negative 12% of the time. Melbourne has a population of 5 million. Suppose that on the 15th of January 2021, there were 50 actual COVID-19 infections in Melbourne. A randomly selected person who lives in Melbourne is given a PCR test. This PCR test is positive. Without any other information about this person, what is the probability that this person has COVID-19? Suppose that on the 15th of January 2022, there were 300,000 actual COVID-19 infections in Melbourne. A randomly selected person who lives in Melbourne is given a PCR test. This PCR test is positive. Without any other information about this person, what is the probability that this person has COVID-19? Based on your answers above, explain why it is important to take the base rate into account when drawing conclusions from the test?

Polymerase chain reaction (PCR) is a method widely used to diagnose COVID-19 infections. Suppose that if a person does not have COVID-19, the test will be negative 84% of the time, and be positive 16% of the time; if the person does have COVID-19, the test will be positive 88% of the time, and be negative 12% of the time. Melbourne has a population of 5 million. Suppose that on the 15th of January 2021, there were 50 actual COVID-19 infections in Melbourne. A randomly selected person who lives in Melbourne is given a PCR test. This PCR test is positive. Without any other information about this person, what is the probability that this person has COVID-19? Suppose that on the 15th of January 2022, there were 300,000 actual COVID-19 infections in Melbourne. A randomly selected person who lives in Melbourne is given a PCR test. This PCR test is positive. Without any other information about this person, what is the probability that this person has COVID-19? Based on your answers above, explain why it is important to take the base rate into account when drawing conclusions from the test?

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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