   Chapter 9.9, Problem 14ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
6 views

# A drug-screening test is used in a large population of people of whom 4% actually use drugs. Suppose that the false positive rale is 3% and the false negative tale is 2%. Thus a person who uses drugs tests positive for them 98% of the time, and a person who does not use drugs tests negative tut them 97% of the time. a.What hat is the probability that a randomly chosen person who tests positive for drugs aclually uses drugs? b.What is the probability that a randomly chosen person who tests negative for drugs does not use drugs?

To determine

To find out the probability that chosen person who tests positive for drugs actually uses drugs.

Explanation

Given information:

In a large population of people 4% actually uses drugs and false positive rate is 3% and false negative rate is 2%. Thus a person who uses drugs and test positive for them 98% of the time and test negative 97% of the time.

Calculation:

Let A= event of choosing the person tests positive for drugs.

E1= event of choosing the person using drugs.

E2= event of choosing the person does not use drugs.

According to the given information the following things can be written

P(E1)=4%P(E2)=96%P(A|E2)=3%P(A¯|E1)=2%P(A|E1

To determine

To find out the probability that chosen person who tests negativefor drugs doesn’t use drugs.

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