The test to detect the presence of the hepatitis b virus is 97% accurate for a person who has the disease and 99% accurate for a person who does not have the disease. in a given population, 0.55% of the people are infected. the probability that a randomly chosen person gets an incorrect result is

0.0055*0.03+0.9945*0.01

because 0.55% people are infected and inaccuracy of the test is 3% 
and rest 99.45% people are not infected and the inaccuracy of the test is 1%

0.03 and 0.01 are the probability of an error being made in infected and uninfected respectively.


0.01011 is the probability that a randomly chosen person gets an incorrect result.