In a certain region of the country it is known from past experiencethat the probability of selecting an adult over 40 years of agewith cancer is 0.05. If the probability of a doctor correctlydiagnosing a person with cancer as having the disease is 0.78 andthe probability of incorrectly diagnosing a person without canceras having the disease is 0.06, what is the probability that aperson is diagnosed as having cancer?
Let A be “having cancer”, A’ be “not having cancer”,
B be “be diagnosed with cancer” and “not be diagnosed withcancer”.
We are given that:
We are looking for P(B).
From total probability rule: