In Example 4.10 on page 164, suppose that the probability that a medical diagnostic test will give a positive result if the disease is not present is reduced from 0.02 to 0.01.
a. If the medical diagnostic test has given a positive result (indicating that the disease is present), what is the probability that the disease is actually present?
b. If the medical diagnostic test has given a negative result (indicating that the disease is not present), what is the probability that the disease is not present?
In Example 4.10
P(D) = 0.03 P(T |D) = 0.90
P(D') = 0.97 P(T | D') = 0.02
Using Equation (4.9) on page 163,

P(TID)P(D) P(TID)P(D) + P(TID')P(D') (0.90) (0.03) (0.02)(0.97) 0.02700.0194 0.0464 (0.90)(0.03) 0.0270 0.0270 - 0.582