Finnegan Pharma has reported that a certain form of its tuberculosis skin test has experienced substantial false-positive and false negative results recently. In a region experiencing an outbreak of this infectious disease, 80% of patients experiencing symptoms and were screened with the Finnegan Pharma skin test administered by medical professionals were noted as testing positive for tuberculosis. However, more comprehensive clinical testing with blood work has shown that, of these patients presenting symptoms and initally diagnosed with tuberculosis, only 60% actually had the infection, a true positive result. Of those who did not test positive with the initial skin test, 75% also tested negative when fully screened with blood work, a true-negative result. [COMMENTS & HINTS: Draw a tree diagram to sort out the information and guide your calculations.]

#8: Given that the full screening results were positive for tuberculosis, what is the probability the patient had an initial positive diagnosis with the Finnegan Pharma skin test?? [COMMENTS & HINTS: Recall that this is a posterior probability question. Enter a rounded answer, rounding only the very last answer to the nearest whole percentage. You should include the percentage symbol.]