KVPY 2020-21 SA Exam Previous Papers

Question : 80 of 80

Marks: +1, -0

In medical diagnostics for a disease, sensitivity (denoted by a) of a test refers to the probability that a test result is positive for a person with the disease, whereas specificity (denoted by b) refers to the probability that a person without the disease tests negative. A diagnostic test for COVID-19 has the values of a = 0.99 and b = 0.99. If the prevalence of COVID-19 in a population is estimated to be 10%, what is the probability that a randomly chosen person tests positive for COVID-19?

0.099
0.10
0.108
0.11

Validate

Solution:

{P}({P}_{{R}})=

Probability of getting positive report

{P}({P}_{{A}})=

Probability of actual COVID-19 positive

{P}(\ov{{P}}_{{A}})=

Probability of not actually COVID-19 positive

{P}({P}_{{R}})={P}({P}_{{R}} \/ {P}_{{A}}) \.{P}({P}_{{A}})+{P}({P}_{{R}} \/ \ov{{P}}_{{A}})

\.{P}(\ov{{P}}_{{A}})

=({99}/{100} \×{10}/{100})+({1}/{100} \×{90}/{100})

={990+90}/{10000}={108}/{1000}=0.108

{P}({P}_{{R}})=0.108

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