It is given that only 0.1 % of a large population have COVID infection. In this population, the reliability of COVID RTPCR-test is specified as follows :
For persons having COVID, 90% of the test detects the disease but 10% goes undetected. For persons not having COVID, 99% of the test is judged COVID negative but 1% are diagnosed as COVID positive.
Based on the above informations, answer the question :
The probability that the selected person will be diagonosed as COVID positive is:
Answer & explanation
Correct answer: option 4
P(person selected will be diagnosed as COVID positive) = P (person does not have COVID and is COVID positive) + P(person has COVID and is COVID positive) = P(does not have COVID) x P(tested COVID positive | does not have COVID) + P(has COVID) x P(tested COVID positive | has COVID)
= P(F). P(GIF) + P(E). P(G|E)
= 0.001 × 0.9 +0.999 × 0.01 = 0.0009 + 0.0099 = 0.01089
Option 4 is correct.