Problem 47 Tuberculosis is a rare disease in developing coun

Problem 4.7. Tuberculosis is a rare disease in developing countries. However, it is the most common cause of death in HIV - positive adults living in these countries (sec [16]). Consider a country in which 0.045% of its adult population has tuberculosis. It is estimated that 8% of all tuberculosis cases in this country are co - infected with HIV. Compute the probability that a randomly selected adult from this country has both tuberculosis and HIV.

Solution

P(both) = P(tuberculosis) * P(HIV | tuberculosis) = 0.00045 * 0.08 = 0.000036