2 5 6C HaP Te r 1 1 ■ C h a n c e sColon Cancer Not Colon Cancer Total
Test Positive
Do Not Test Positive
Total 100,000This population size represents the total number of people who are tested.
We have no information about the ones who are not tested, so they cannot
figure into our calculations.
The bottom row can now be filled in by dividing the total population into
those who have colon cancer and those who do not have colon cancer. Just
multiply the population size by the probability of colon cancer in the gen-
eral population [Pr(h)] to get a number for the second box on the bottom
row. This figure represents the total number of people with colon cancer in
this population. Then subtract that product from the population size and
put the remainder in the remaining box. This represents the total number
of people without colon cancer in this population. Since these two groups
exhaust the population, they must add up to the total population size. In our
case, we were given that the probability that a person in the general popula-
tion has colon cancer is 0.003. On this basis, we can fill in the bottom row of
the table:Colon Cancer Not Colon Cancer Total
Test Positive
Do Not Test Positive
Total 300 99,700 100,000Next, fill out the second column by dividing the total number of people
with colon cancer into those who test positive and those who do not test
positive. These numbers can be calculated with the given conditional prob-
ability of testing positive, given colon cancer [Pr(e|h)]. In our example, if a
person has colon cancer, the probability that the test is positive is 0.9. Thus,
270 ( 5 0.9 3 300) of the people in the colon cancer column will test positive
and the rest (300 – 270 5 30) will not, so we get these figures:Colon Cancer Not Colon Cancer Total
Test Positive 270
Do Not Test Positive 30
Total 300 99,700 100,00097364_ch11_ptg01_239-262.indd 256 15/11/13 10:58 AM
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