Refer to the sample data for a pre-employment drug screening shown below. If one of the subjects is randomly selected, find the following probabilities (rounded to 4 decimal places):

Question

Refer to the sample data for a pre-employment drug screening shown below. If one of the subjects is randomly selected, find the following probabilities (rounded to 4 decimal places):

	Positive Test Result	Negative Test Result
Uses Drugs	44	6
Not a Drug User	18	38

a) What is the probability that the test result is a false positive? 

b) Find the probability of getting someone who tests negative, given that he or she is not a drug user. 

c) Who would suffer from a false positive result? Why? 

Answer 1

ok, so a false positive is when the drug test gives a positive result, but the person tested isn't a drug user (which answers part c!). To calculate this, we divide the number of false positives, which here is 18, by the number of false positives plus true negatives, which is 18 + 38. So 18/56 = 0.3214.

Next, we want the probability of someone getting a negative test result, given that they are not a drug user. So that's basically the inverse of the previous: we want 38/56, which is 0.6786.

Hope that helps!