taiwan-gsat 2022 Q5

taiwan-gsat · Other · gsat__math-a 5 marks Conditional Probability Bayes' Theorem with Diagnostic/Screening Test
It is known that 30\% of the population in a certain region is infected with a certain infectious disease. For a rapid screening test of the disease, there are two results: positive or negative. The test has an 80\% probability of identifying an infected person as positive and a 60\% probability of identifying an uninfected person as negative. To reduce the situation where the test incorrectly identifies an infected person as negative, experts recommend three consecutive tests. If $P$ is the probability that an infected person is among those who test negative in a single test, and $P'$ is the probability that an infected person is among those who test negative in all three consecutive tests, what is $\frac { P } { P' }$ closest to?
(1) 7
(2) 8
(3) 9
(4) 10
(5) 11
It is known that 30\% of the population in a certain region is infected with a certain infectious disease. For a rapid screening test of the disease, there are two results: positive or negative. The test has an 80\% probability of identifying an infected person as positive and a 60\% probability of identifying an uninfected person as negative. To reduce the situation where the test incorrectly identifies an infected person as negative, experts recommend three consecutive tests. If $P$ is the probability that an infected person is among those who test negative in a single test, and $P'$ is the probability that an infected person is among those who test negative in all three consecutive tests, what is $\frac { P } { P' }$ closest to?\\
(1) 7\\
(2) 8\\
(3) 9\\
(4) 10\\
(5) 11