Question

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. If 0.55% of the people in a given population are infected, what is the probability that a randomly chosen person gets an incorrect result?. . 0.98455. . 0.000165. . 0.009945. . 0.001011

Answer 1

The probability tests to detect the presence of hepatitis B:
P (presence)= 0.97 (true) 0.03 (false)
P (absence)= 0.99 (true) 0.01 (false)

P(infected)=0.0055
P(not infected)= 0.9945

To have an incorrect result:
P[infected and false from P(presence)] + P[not infected and false from P(absence)]

=0.0055*0.03+0.9945*0.01= 0.01011

The answer is 0.01011