Question

4. given the following information answer the ensuing.

- 20% of the population is estimated to be infected

- a diagnostic test indicates infection 60% of the time in testing an infected person

- a diagnostic test indicates no infection 80% of the time in testing a non-infected person

4.1 probability a person is infected given that the test indicates infection

4.2 probability a person is not infected given that the does not indicate infection

4.3 probability a person is infected and the test indicates infection

4.4 probability a person is infected or the test indicates infection

Answer 1

4.1)

probability a person is infected given that the test indicates infection

=P(infected and test indicates infection)/P(test indicates infection)

=0.2*0.6/(0.2*0.6+(1-0.2)*(1-0.8))=0.4286

4.2)probability a person is not infected given that the does not indicate infection

=P(not infected and test indicates no infection)/P(test indicates no infection)

=(1-0.2)*0.8/((1-0.2)*0.8+0.2*(1-0.6))=0.8889

4.3)

probability a person is infected and the test indicates infection=0.2*0.6=0.12

4.4)

probability a person is infected or the test indicates infection =1-P(not infected and test not shows infection)=1-(1-0.20)*0.8=0.36