One way to detect if someone has been infected by a virus is to test if they have antibodies in their system. While antibody tests (serological testing) can be relatively precise, it may be the case that the virus has not been present long enough in a person's system for the body to have generated enough antibodies to be detected in the blood. Additionally, different antibodies may share similar biochemical features, and this means the test may indicate the antibody of interest is present because a different virus resulted in comparable antibodies. Thus, the test will indicate the antibodies as present even if the antibody for this particular virus is not actually present. Here is a contingency table for patients that were tested for the virus using this antibody test. This table summarizes whether the patient was or wasn't actually infected, and what the results of the initial antibody test were. Virus Infection Status (A) Test Results (B) A1 = Infected A2 - Not Infected Totals B1 = Positive Test 5,014 57,289 62,303 B2 = Negative 285 851,412 851,697 Test Totals 5,299 908, 701 914,000 We will use this sample data as a model for the corresponding proportions in the population. Using this information, calculate the following probabilities: . P(A] ) = . P(B1) = . P(B1 | A2) = . P(B2 | A1) =