Chapter 8.4, Problem 60E

Tuberculosis screening. A test for tuberculosis was given to $1,000$ subjects, $8\%$ of whom were known to have tuberculosis. For the subjects who had tuberculosis, the test indicated tuberculosis in 90% of the subjects, was inconclusive for $7\%$, and indicated no tuberculosis in $3\%$. For the subjects who did not have tuberculosis, the test indicated tuberculosis in $5\%$ of the subjects, was inconclusive for $10\%$, and indicated no tuberculosis in the remaining $85\%$. What is the probability of a randomly selected person having tuberculosis given that the test indicates tuberculosis? Of not having tuberculosis given that the test was inconclusive?