Question

The table below shows the results from a test for marijuana use, provided by a certain drug testing company.

Actually Used Marijuana	No	Yes
Positive Test Result	32	103
Negative Test Result	156	6

1. How many subjects had false positive results?
2. How many subjects had false negative results?
3. What is the probability that a randomly selected person actually did not use marijuana?
4. What is the probability that a randomly selected person actually used marijuana give they had a positive test result?

Answer 1

a. How many subjects had false positive results

False positive means test result which wrongly indicates that a particular condition or attribute is present.

The person actually not used Marijuana but the test result is positive .

Actually Used Marijuana	No	Yes
Positive Test Result	32	103
Negative Test Result	156	6

From the above table that value is : 32

Number of subjects had false positive results = 32

b. How many subjects had false negative results?

false negative

a test result which wrongly indicates that a particular condition or attribute is absent.

i.e The person actually used Marijuana but the test result is negative.

Actually Used Marijuana	No	Yes
Positive Test Result	32	103
Negative Test Result	156	6

From the above table that value is : 6

Number of subjects had false negative results = 6

c. Probability that a randomly selected person actually did not use marijuana

Actually Used Marijuana	No	Yes	Total
Positive Test Result	32	103	135
Negative Test Result	156	6	162
Total	188	109	297

From the above table ,

Total number of persons who actually did not use Marijuana = 188

Total number of persons = 297

Probability that a randomly selected person actually did not use marijuana

= Total number of persons who actually did not use Marijuana / Total number of persons= 188/297

Probability that a randomly selected person actually did not use marijuana = 188/297=0.633

d. Probability that a randomly selected person actually used marijuana give they had a positive test result

Actually Used Marijuana	No	Yes	Total
Positive Test Result	32	103	135
Negative Test Result	156	6	162
Total	188	109	297

From the above table

Total Number of persons who had a positive result = 135

Number of persons who had actually used marijuana and had a positive test result = 103

Probability that a randomly selected person actually used marijuana give they had a positive test result

= Number of persons who had actually used marijuana and had a positive test result / Total Number of persons who had a positive result

= 103/135

Probability that a randomly selected person actually used marijuana give they had a positive test result = 103/135=0.763