In order to evaluate the rate of error experienced in reading chest x-rays, the following experiment is done. Several people with known tuberculosis (TB) status (through other reliable tests) are subjected to chest x-rays. A technician who is unaware of this status reads the x-ray, and Table gives the result. Here +x-ray means the technician concluded that the person has TB.
|
Table
|
|
|
Person without TB
|
Person with TB
|
Total
|
|
+X-ray
|
70
|
27
|
97
|
|
-X-ray
|
1883
|
20
|
1903
|
|
Total
|
1945
|
55
|
2000
|
Find (a) P(TB|+ X - ray), (b) P(+X - ray|No TB), and (c) P(No TB|- X - ray).