+0  
 
0
54
1
avatar

A test for tuberculosis was given to 1000 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 negative for 3%. For the subjects who did not have tuberculosis, the test indicated tuberculosis in 5%, was inconclusive for 10%, and was negative for the remaining 85%. What is the probability of a randomly selected person having tuberculosis given that the test indicates tuberculosis

 Feb 18, 2020
 #1
avatar+6180 
+1

\(P[\text{tuberculosis|positive test}] = \dfrac{P[\text{positive test|tuberculosis}]P[\text{tuberculosis}]}{P[\text{positive test}]} = \\ \dfrac{0.9\cdot 0.08}{0.9 \cdot 0.08 + 0.05\cdot 0.92} \approx 0.939948 \\ \)

.
 Feb 19, 2020

47 Online Users

avatar
avatar
avatar
avatar
avatar
avatar