Question

1.

(3 pts) All interns for Comcast are required to be tested for drug use. The imperfect test

gives positive results (indicating drug use) for 80% of all interns who actually use drugs

but also (incorrectly) for 3% of those who do not use drugs. Suppose that only 10% of all

of these interns actually use drugs. If an intern is tested negative, what is the probability

that he/she uses drugs?

Answer 1

From the given data, the following Table is calculated:

	Test positive	Test negative	Total
Use drugs	0.10 X 0.80 = 0.08	0.10 - 0.08 = 0.02	0.10
Does not use drug	0.90 X 0.03 = 0.027	0.90 - 0.027 = 0.873	1 - 0.10 = 0.90
Total	0.107	0.893	1.00

P(Use drugs/ Test negative) = P(Use drugs AND Test negative) / P(Test negative)

                                        = 0.02/0.893 = 0.0224

So,

If an intern is tested negative, the probability that he/she uses drugs = 0.0224

So,

Answer is:

0.0224