   Chapter 9.9, Problem 15ES ### 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
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# Two different factories both produce a certain automobile part The probability that a component from the first factory is detective is 2%. and the probability that a component from the second factory is defective is 3%. In a supply of 180 of the parts, 100 were obtained from the first factor y and 80 from the second factory. a.What is the probability that a part chosen at random from the 180 is from the fust factor)? b.What is the probability that a part chosen at random from the 180 is from the second factory? c.What is the ptohahility that a part chosen at random from the 180 is defective? d.If the chosen part is defective, what is the probability that it came from the first factory?

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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