1. A certain drug test has a 10% false positive rate (a positive test even if...
1. A certain drug test has a 10% false positive rate (a positive test even if the person has not used that drug) and a 15% false negative rate (a negative test despite the person using the drug). It is known that approximately95% of people do not use the drug being tested for. If 10,000 people are given the test, complete the table with the expected results and then answer the following questions. Test Results Positive Negative Total No Drug Use Drug Use Total 10000
(a) Find P(Positive and Drug Use)
(b) Find P(Negative and No Drug Use)
(c) Find P(No Drug Use|Negative)
(d) Find P(Drug Use|Positive)
(e) A random person tests positive. What is the likelihood that the person is using the drug?
Homework Answers
Ans:
| Positive | Negative | Total | |
| No drug use | 950 | 8550 | 9500 |
| drug use | 425 | 75 | 500 |
| Total | 1375 | 8625 | 10000 |
a)P(positive and drug use)=425/10000=0.0425
b)P(Negative and No Drug Use)=8550/10000=0.8550
c)P(no drug use/negative)=8550/8625=0.9913
d)P(drug use/positive)=425/1375=0.3091
e)P(using the drug/test positive)=425/1375)=0.3091
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