ase-Study 2: Read the following passage and answer the questions given below.
The reliability of a COVID PCR test is specified asfollows: Of people having COVID, 90% of the test detectsthe disease but 10% goes undetected. Of peoplefree of COVID, 99% of the test is judged COVIDnegative but 1% are diagnosed as showing COVIDpositive. From a large population of which only0.1% have COVID, one person is selected atrandom, given the COVID PCR test, and thepathologist reports him/her as COVID positive.
(i) What is the probability of the ‘person to be testedas COVID positive’ given that ‘he is actuallyhaving COVID’?
(ii) What is the probability of the ‘person to be tested as COVID positive’ given that ‘he is actually nothaving COVID’?
(iii)What is the probability that the ‘person is actuallynot having COVID’?

Question

ase-Study 2: Read the following passage and answer the questions given below.
The reliability of a COVID PCR test is specified asfollows: Of people having COVID, 90% of the test detectsthe disease but 10% goes undetected. Of peoplefree of COVID, 99% of the test is judged COVIDnegative but 1% are diagnosed as showing COVIDpositive. From a large population of which only0.1% have COVID, one person is selected atrandom, given the COVID PCR test, and thepathologist reports him/her as COVID positive.
(i) What is the probability of the ‘person to be testedas COVID positive’ given that ‘he is actuallyhaving COVID’?
(ii) What is the probability of the ‘person to be tested as COVID positive’ given that ‘he is actually nothaving COVID’?
(iii)What is the probability that the ‘person is actuallynot having COVID’?

Accepted Answer

Case Study 1: AnswerConsider the events E1 = People having COVID, E2 = People free of COVID A = Person to be tested as COVID positive (i) Probability of the ‘person to be tested as COVID positive’ given that he is actually having COVID                                  PAE1=90%=90100=0.9(ii) Probability of the ‘person to be tested as COVID positive’ given that he is actually not having COVID                                PAE1=90%=90100=0.9(iii) Probability that the person is actually not having COVID = P(E2 ) = 99.9%=9991000=0.999

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