Question

In any given year, 3% of heavy smokers develop lung cancer. Computed tomography (CT) scans correctly identify lung cancer 89% of the time and correctly provide a negative result for 93% of individuals without lung cancer.

a) Draw a probability tree that represents the above situation and compute the probability for each of the four possible outcomes.
b) In total, what proportion of all CT test results are accurate?
c) In total, what proportion of all CT test results are not accurate?

d) If a heavy smoker gets a positive CT test result, what is the probability that they truly have lung cancer?
e) If a heavy smoker gets a negative CT test result, what is the probability that they truly do not have lung cancer?

Answer 1

a)

	Diagnosed CT scan	Not Diagnosed	Total
Cancer	0.0267	0.0033	0.03
Not Cancer	0.0679	0.9021	0.97
Total	0.0946	0.9054	1

b) Accurate Proportion from table : total accurate/ total = (0.0267 + 0.9021)/1 = 0.9288

c)Not Accurate Proportion from table : total Not accurate/ total = (0.0679+0.0033)/1 = 0.0712

d)P(cancer| diagnosed) =  0.0267/0.0946 = 0.2822

e) P(not cancer| not diagnosed) = 0.9021/0.9054 = 0.9964