Question

	Test shows drug use	Test shows no drug use	Total
Subject uses drugs	90	4,995	5,085
Subject does not use drugs	10	94,905	94,915
Total	100	99,900	100,000

Determine the probabilities, based on the table:

A) Selecting a person that does not use drugs or the test shows no drug use

B) Selecting a person that uses drugs and the test shows drug use

C) Selecting a person that does not use drugs, given that the test shows no drug use

D) Selecting a person that does not use drugs, given that the test shows drug use

E) Selecting a person that obtained a positive test result (test shows drug use), given that the person does not use drugs

Answer 1

Using above table we find the following probabilities,

a) P(Subject does not use drugs or test shows no drug use)

= (94915/100000) + (99900/100000) - (94905/100000)

= (94915 + 99900 - 94905)/100000

= 99910/100000

= 0.9991

Therefore, required probability is 0.9991

b) P(Subject uses drug and Test shows drug use)

= 90/100000

= 0.0009

Therefore, required probability is 0.0009

c) P(Subject does not use drugs | Test shows no drug use)

= 94905/99900

= 0.95

Therefore, required probability is 0.95

d) P(Subject does not use drugs | Test shows drug use)

= 10/100

= 0.1

Therefore, required probability is 0.1

e) P(Test shows drug use | Subject does not use drugs)

= 10/94915

= 0.00010536

Therefore, required probability is 0.0001