Question

18. Imagine that coronavirus has a 0.002% incidence in the population. A test for the virus has a 0.001% false positive rate and no false negative rate (false positive rate means the chance that if an uninfected individual takes the test the test will falsely identify them as infected). If a random person takes the test and gets a positive result, what is the chance that they are infected? (Show your work to earn partial credit) (4 points) Now consider the case in the future, where the incidence of the virus has increased to 1%. Now if a random person takes the test and gets a positive result, what is the chance that they are infected? (2 points)

Answer 1

answer : Given conditions in question are for test of coronavirus : 0.001 false positive rate and no false negative rate. Incidence are 0.001% and 1 % For both scenarios following is the calculation.

Answer: Given cozona vizus incidents in population ( Total Number) = 0.0024. false positive zate of Test = 0.001%. chance of Healthy person tested as infected False positive Rate False positive + Total Number 0.001 y. 0.001%+0.0024. -0.001 0.003 = For total incidences 0.002./. = 0.3% Chances of person being zeally infected = 1 – 0.3.4. = 0.77 0.3.4 being False tre je Random person - Test 0.71. being infected. Now for total number / incidence in future = 1%. chance of Healthy person tested as infected False positive Rate false positive + Total Number 0.00ly. 0.001% + 1%. 0.001 1.001 0.0009 %. Chance of Healthy person tested 'as infected = Chances of person being zeally infected = 1 – 0.0009 for total incidences 1% = 0.9991 % 0.000g./. False tre. je Random person - Tests < - 0.9991.f being infected.