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. In a given population, 0.55% of the people are infected. The probability that a randomly chosen person gets an incorrect result is

Answer 1

The required probability is 0.01011

Explanation:

The test to detect the presence of hepatitis B is 97% accurate

Probability of presence and true = 0.97

Probability of presence and false = 0.03

The test to detect the absence of hepatitis B is 99% accurate

Probability of absence and true = 0.99

Probability of absence and false = 0.01

Probability of infected = 0.55% = 0.0055

Probability of not infected = 1 - 0.0055 = 0.9945

Probability to have an incorrect result : P(infected) and P(presence and false) + P(not infected) and P(absence and false)

= 0.0055 × 0.03 + 0.9945 × 0.01

= 0.01011

Hence, The required probability is 0.01011

Answer 2

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.