Suppose that 90 percent of women who are Krista's age do not have high cholesterol and 10 percent do. If a cholesterol test indicates that Krista has high cholesterol, but the test is only accurate 80 percent of the time, then the probability that Krista really does have high cholesterol is roughly:
A)90 percent.
B)80 percent.
C)31 percent.
D)18 percent.

Question

Quizplus · Accepted Answer

For every 100 people who are Krista's age who take the test, 90 of them do not have high cholesterol, and 10 of them do. Since the test is accurate 80 percent of the time, the test will incorrectly identify 0.2 × 90 = 18 as not having high cholesterol and correctly identify 0.8 × 10 = 8 as having high cholesterol. So if 8 of every 26 people who test positive for high cholesterol actually have high cholesterol, then Krista's probability of having high cholesterol is 8/26, or roughly 31 percent.

Suppose That 90 Percent of Women Who Are Krista's Age