Suppose that only 2 percent of all people are geniuses. If an IQ test indicates that Albert is a genius, but the test is only accurate 90 percent of the time, then the probability that Albert really is a genius is roughly:
A)18 percent.
B)2 percent.
C)10 percent.
D)16 percent

Question

Quizplus · Accepted Answer

For every 100 people who take an IQ test, 2 of them are geniuses and 98 of them are not. Since the test is accurate 90 percent of the time, the test will incorrectly identify 0.1 × 98 = 9.8 as being a genius and correctly identify 0.9 × 2 = 1.8 as being a genius. So if 1.8 out of every 11.6 people who the test indicates are a genius actually are geniuses, then Albert's probability of being a genius is 1.8/11.6, or roughly 16 percent.

Suppose That Only 2 Percent of All People Are Geniuses