The reliability of a COVID PCR test is specified as follows:
Of people having COVID, 90% of the test detects the disease but 10% goes undetected. Of people free of COVID, 99% of the test is judged COVID negative but 1% are diagnosed as showing COVID positive. From a large population of which only 0.1% have COVID, one person is selected at random, given the COVID PCR test, and the pathologist reports him/her as COVID positive.
The reliability of a COVID PCR - Teachoo.jpg

Based on the above information, answer the following:

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Question 1

What is the probability of the ‘person to be tested as COVID positive’ given that ‘he is actually having COVID?

(a) 0.001

(b) 0.1

(c) 0.8

(d) 0.9

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Question 2

What is the probability of the ‘person to be tested as COVID positive’ given that ‘he is actually not having COVID’?

(a) 0.01

(b) 0.99

(c) 0.1

(d) 0.001

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Question 3

What is the probability that the ‘person is actually not having COVID?

(a) 0.998

(b) 0.999

(c) 0.001

(d) 0.111

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Question 4

What is the probability that the ‘person is actually having COVID given that ‘he is tested as COVID positive’?

(a) 0.83

(b) 0.0803

(c) 0.083

(d) 0.089

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Question 5

What is the probability that the ‘person selected will be diagnosed as COVID positive’?

(a) 0.1089

(b) 0.01089

(c) 0.0189

(d) 0.189

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  1. Chapter 13 Class 12 Probability (Term 2)
  2. Serial order wise

Transcript

Question The reliability of a COVID PCR test is specified as follows: Of people having COVID, 90% of the test detects the disease but 10% goes undetected. Of people free of COVID, 99% of the test is judged COVID negative but 1% are diagnosed as showing COVID positive. From a large population of which only 0.1% have COVID, one person is selected at random, given the COVID PCR test, and the pathologist reports him/her as COVID positive. Based on the above information, answer the following:Question 1 What is the probability of the ‘person to be tested as COVID positive’ given that ‘he is actually having COVID? (a) 0.001 (b) 0.1 (c) 0.8 (d) 0.9(d) 0.9 Question 2 What is the probability of the ‘person to be tested as COVID positive’ given that ‘he is actually not having COVID’? (a) 0.01 (b) 0.99 (c) 0.1 (d) 0.001 (a) 0.01 Question 3 What is the probability that the ‘person is actually not having COVID? (a) 0.998 (b) 0.999 (c) 0.001 (d) 0.111 (b) 0.999 Question 4 What is the probability that the ‘person is actually having COVID given that ‘he is tested as COVID positive’? (a) 0.83 (b) 0.0803 (c) 0.083 (d) 0.089(c) 0.083 Question 5 What is the probability that the ‘person selected will be diagnosed as COVID positive’? (a) 0.1089 (b) 0.01089 (c) 0.0189 (d) 0.189(b) 0.01089

About the Author

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.