(Im down to the last question on my homework but I\'m stumped on this one....).
ID: 3130809 • Letter: #
Question
(Im down to the last question on my homework but I'm stumped on this one....).
Suppose a certain drug test is 95% sensitive, that is, the test will correctly identify a drug user as testing positive 95% of the time, and 90% specific, that is, the test will correctly identify a non-user as testing negative 90% of the time.
Suppose a corporation decides to test its employees for drug use, and that only 0.8% of the employees actually use the drug. What is the probability that, given a positive drug test, an employee is actually a drug user? Let D
stand for being a drug user and N indicate being a non-user. Let be the event of a positive drug test and
be the event of a negative drug test.
(b) P(N)=
Answer
(d) P(|N)=
Answer
(e) P()=
Answer
(f) P(D|)=
Answer
Explanation / Answer
b)
Here, by Bayes' Rule,
P(N) = 1 - P(D) = 1 - 0.008 = 0.992 [ANSWER]
*******************
d)
Hence,
P(+|N) = 1- 0.90 = 0.10 [ANSWER]
*******************
e)
By Bayes' Rule,
P(+) = P(D) P(+|D) + P(D') P(+|D') = 0.008*0.95 + (1-0.008)*(1-0.90) = 0.1068 ANSWER]
*********************
f)
Hence,
P(D|+) = P(D) P(+|D)/P(+) = 0.008*0.95/0.1068 = 0.071161049 [ANSWER]
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