1.9% of a population is infected with a certain disease.There is a test for the disease; however,the test is not completely accurate.91% of those who have the disease will test positive.However 3.6% of those who do not have the disease will also test positive (false positives).What is the probability that any given person will test positive? Round your answer to three decimal places if necessary.
A)0.910
B)0.017
C)0.053
D)0.035
E)0.473

Question

Quizplus · Accepted Answer

We need to use Bayes' theorem to calculate the probability of testing positive. Let A be the event that a person has the disease, and B be the event that a person tests positive. Then, 
P(B) = P(B|A)P(A) + P(B|not A)P(not A)
= 0.91*0.019 + 0.036*0.981
= 0.053 (rounded to three decimal places)

19% of a Population Is Infected with a Certain Disease