A PCR test is commonly used for diagnosing a viral infection. It has a false positive rate (indicating infection where there is none) of 5% and a false negative rate of 25 %. Patients take two tests and if either is positive then an infection is declared. If the actual incidence of the infection is currently two hundred in a hundred thousand, what is the probability that: i) Someone who is declared virus - negative is in fact infected? ii) One or more of ten people tested and allowed on a flight are in fact infected despite screening negative for the virus?
A PCR test is commonly used for diagnosing a viral infection. It has a false positive rate (indicating infection where there is none) of 5% and a false negative rate of 25 %. Patients take two tests and if either is positive then an infection is declared. If the actual incidence of the infection is currently two hundred in a hundred thousand, what is the probability that: i) Someone who is declared virus - negative is in fact infected? ii) One or more of ten people tested and allowed on a flight are in fact infected despite screening negative for the virus?
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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Transcribed Image Text:A PCR test is commonly used for diagnosing a viral infection. It has a false positive
rate (indicating infection where there is none) of 5% and a false negative rate of 25 %. Patients
take
two tests and if either is positive then an infection is declared. If the actual incidence of the
infection
is currently two hundred in a hundred thousand, what is the probability that:
i) Someone who is declared virus - negative is in fact infected?
ii) One or more of ten people tested and allowed on a flight are in fact infected despite screening
negative for the virus?
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