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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
1945
55
2000
Find (a) P(TB|+ X - ray), (b) P(+X - ray|No TB), and (c) P(No TB|- X - ray).
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