Answer to Question #128156 in Statistics and Probability for mahi

Question

One half percent of the population has CORONA. There is a test to detect CORONA.A
positive test result is supposed to mean that you have CORONA(but the test is not
perfect).For people with CORONA, the test misses the diagnosis by 2% of the times and
for the people without CORONA, the test incorrectly tells 3% of them that they have
CORONA. What is the probability that you have CORONA, given that your test comes
back positive?

Answer 1

By the Bayes Theorem:

$P=\frac{0.005*0.98}{0.005*0.98+0.995*0.03}=0.1410.$