PROBLEM 2.22
The best way to start this problem is to write out and draw what you’re given. After
reading the question once, we know the following information:
3%
predisposed
99% test (+)
?
98% test (-)
PROBLEM 2.22 (CONT.)
With the information we’re given, we are able to calculate the rest of the information
we are not given.
A. 1 - .03 = .97
B. 1 - .99 = .01
C. 1 - .98 = .02
99% test (+)
3%
predisposed
B.
C.
A.
1% test (-)
2% test (+)
97% not
predisposed
98% test (-)
PROBLEM 2.22 (CONT)
Next, we find the product of each possibility by multiplying through each branch.
A. .03 x .99 = .03
B. .03 x .01 – 0.00
C. .97 x .02 – 0.02
D. .97 x .98 = 0.95
99% test (+)
A. 0.03
1% test (-)
B. 0.00
2% test (+)
C. 0.02
98% test (-)
D. 0.95
3%
predisposed
97% not
predisposed
PROBLEM 2.22
Question: What is the probability that a randomly selected person who tests positive
for the predisposition actually has the predisposition?
Here we want to look at 2 different values. We know that 0.03 people test positive for
the predisposition, and that (0.03 + 0.02 = 0.05) actually have the
predisposition. Therefore:
0.03 / 0.05 =
60%
Actually have the predisposition