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In-this-covid-19-pandemic-it-is-known-that-are-5-667-355-confirmed-cases-out-of-273-500-000-in-X-country-population-based-WHO-One-of-the-equipment-to-test-the-covid-19-is-GeNose-C19-S-deve




Question Number 206514 by cortano21 last updated on 17/Apr/24
 In this covid −19 pandemic, it is    known that are 5,667,355 confirmed    cases out of 273,500,000 in X country   population based WHO.    One of the equipment to test the   covid−19 is GeNose C19−S developed   by UGM. GeNose C19−S is a rapid   screening equipment for Sars−CoV2   virus infection through the breath   of Covid −19 patient . It is claim   that the sensivity of the test is 0,90   that is, if a person has the disease,    then the probability that the diagnostic   blood test comes back positive   is 0,90. In addition , the specificity   of the test is 0,95, i.e if a person    is free the disease, then the probability   that the diagnostic test comes back   negative is 0,95.    Let D and H is the event that a    randomly selected individual has   the disease and disease−free    (healty), respectively.   a. What is the positive predictive     value of the GeNose C19−S test?    That is, given that the blood test    is positive for disease, what is the   probability that person actually has    the disease?       b. If the doctor perfoms the test for   the second time , taking P(D) equals   to the value of probability you   obtained from part a), determine    the update positive predictive     value of the test.
$$\:{In}\:{this}\:{covid}\:−\mathrm{19}\:{pandemic},\:{it}\:{is}\: \\ $$$$\:{known}\:{that}\:{are}\:\mathrm{5},\mathrm{667},\mathrm{355}\:{confirmed}\: \\ $$$$\:{cases}\:{out}\:{of}\:\mathrm{273},\mathrm{500},\mathrm{000}\:{in}\:{X}\:{country} \\ $$$$\:{population}\:{based}\:{WHO}.\: \\ $$$$\:{One}\:{of}\:{the}\:{equipment}\:{to}\:{test}\:{the} \\ $$$$\:{covid}−\mathrm{19}\:{is}\:{GeNose}\:{C}\mathrm{19}−{S}\:{developed} \\ $$$$\:{by}\:{UGM}.\:{GeNose}\:{C}\mathrm{19}−{S}\:{is}\:{a}\:{rapid} \\ $$$$\:{screening}\:{equipment}\:{for}\:{Sars}−{CoV}\mathrm{2} \\ $$$$\:{virus}\:{infection}\:{through}\:{the}\:{breath} \\ $$$$\:{of}\:{Covid}\:−\mathrm{19}\:{patient}\:.\:{It}\:{is}\:{claim} \\ $$$$\:{that}\:{the}\:{sensivity}\:{of}\:{the}\:{test}\:{is}\:\mathrm{0},\mathrm{90} \\ $$$$\:{that}\:{is},\:{if}\:{a}\:{person}\:{has}\:{the}\:{disease},\: \\ $$$$\:{then}\:{the}\:{probability}\:{that}\:{the}\:{diagnostic} \\ $$$$\:{blood}\:{test}\:{comes}\:{back}\:{positive} \\ $$$$\:{is}\:\mathrm{0},\mathrm{90}.\:{In}\:{addition}\:,\:{the}\:{specificity} \\ $$$$\:{of}\:{the}\:{test}\:{is}\:\mathrm{0},\mathrm{95},\:{i}.{e}\:{if}\:{a}\:{person}\: \\ $$$$\:{is}\:{free}\:{the}\:{disease},\:{then}\:{the}\:{probability} \\ $$$$\:{that}\:{the}\:{diagnostic}\:{test}\:{comes}\:{back} \\ $$$$\:{negative}\:{is}\:\mathrm{0},\mathrm{95}.\: \\ $$$$\:{Let}\:{D}\:{and}\:{H}\:{is}\:{the}\:{event}\:{that}\:{a}\: \\ $$$$\:{randomly}\:{selected}\:{individual}\:{has} \\ $$$$\:{the}\:{disease}\:{and}\:{disease}−{free}\: \\ $$$$\:\left({healty}\right),\:{respectively}. \\ $$$$\:{a}.\:{What}\:{is}\:{the}\:{positive}\:{predictive}\: \\ $$$$\:\:{value}\:{of}\:{the}\:{GeNose}\:{C}\mathrm{19}−{S}\:{test}? \\ $$$$\:\:{That}\:{is},\:{given}\:{that}\:{the}\:{blood}\:{test}\: \\ $$$$\:{is}\:{positive}\:{for}\:{disease},\:{what}\:{is}\:{the} \\ $$$$\:{probability}\:{that}\:{person}\:{actually}\:{has} \\ $$$$\:\:{the}\:{disease}?\: \\ $$$$\: \\ $$$$\:{b}.\:{If}\:{the}\:{doctor}\:{perfoms}\:{the}\:{test}\:{for} \\ $$$$\:{the}\:{second}\:{time}\:,\:{taking}\:{P}\left({D}\right)\:{equals} \\ $$$$\:{to}\:{the}\:{value}\:{of}\:{probability}\:{you} \\ $$$$\left.\:{obtained}\:{from}\:{part}\:{a}\right),\:{determine}\: \\ $$$$\:{the}\:{update}\:{positive}\:{predictive}\: \\ $$$$\:\:{value}\:{of}\:{the}\:{test}.\: \\ $$

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