A certain affects vírus 06% of the population. A test used to detect the virus i

Question

A certain affects vírus 06% of the population. A test used to detect the virus in a person is positive 90% of the time if the person has the virus (true positive) and 12% of the time if the person does not have the virus (false postive). Fill out the remainder of the following table and use it to answer the two questions below Infected Not Infected Total Positive Test Negative Test Total 600 99,400 100,000 a) Find the probability that a person has the virus given that they have tested positive. Round your answer to the nearest tenth of a percent and do not include a percent sign. | P(infected | Positive Test)-| b) Find the probability that a person does not have the virus given that they test negative. Round your answer to the nearest tenth of a percent and do not |% include a percent sign. P(Not Infected | Negative Test)-| |%

Explanation / Answer

                              Infected                                Not infected                   Total

Positive test                540                                    11928                               12468

Negative test              60                                       87472                              87532

Total                           600                                       99400                           100000

a) P(infected | positive test) = P(infected and positive test)/P(positive test)

                                                           = 540/12468 = 0.043 = 4.3%

b) P(Not infected | Negative test) = P(Not infected and negative test)/P(Negative test)

                                                     = 87472/87532 = 0.999 = 99.9%

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