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Problem 4 The International Olympic Committee wanted to ensure that the competition in the 2008 Olympic Games was as fair as possible. So, the committee administered more than 5000 drug tests. All medal winners were tested, as well as other randomly selected competitors. Suppose that 2% of athletes had actually taken banned drugs. No drug test is perfect. Sometimes the test is positive, indicating that an athlete took drugs, but the athlete actually didn't. We call this a false positive result. Other times, the drug test is negative, but the athlete actually took drugs. This is called a false negative result. Suppose that the testing procedure used at the Olympics has a false positive rate of 1% and a false negative rate of 0.5%. A) Find the probability that a randomly-tested athlete will have a positive test. B) If an athlete has a positive test, what is the probability that they actually use drugs?

Problem 4 The International Olympic Committee wanted to ensure that the competition in the 2008 Olympic Games was as fair as possible. So, the committee administered more than 5000 drug tests. All medal winners were tested, as well as other randomly selected competitors. Suppose that 2% of athletes had actually taken banned drugs. No drug test is perfect. Sometimes the test is positive, indicating that an athlete took drugs, but the athlete actually didn't. We call this a false positive result. Other times, the drug test is negative, but the athlete actually took drugs. This is called a false negative result. Suppose that the testing procedure used at the Olympics has a false positive rate of 1% and a false negative rate of 0.5%. A) Find the probability that a randomly-tested athlete will have a positive test. B) If an athlete has a positive test, what is the probability that they actually use drugs?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Problem 4 The International Olympic Committee wanted to ensure that the competition in the 2008 Olympic Games was as fair as possible. So, the committee administered more than 5000 drug tests. All medal winners were tested, as well as other randomly selected competitors. Suppose that 2% of athletes had actually taken banned drugs. No drug test is perfect. Sometimes the test is positive, indicating that an athlete took drugs, but the athlete actually didn't. We call this a false positive result. Other times, the drug test is negative, but the athlete actually took drugs. This is called a false negative result. Suppose that the testing procedure used at the Olympics has a false positive rate of 1% and a false negative rate of 0.5%. A) Find the probability that a randomly-tested athlete will have a positive test. B) If an athlete has a positive test, what is the probability that they actually use drugs?
Transcribed Image Text:Problem 4 The International Olympic Committee wanted to ensure that the competition in the 2008 Olympic Games was as fair as possible. So, the committee administered more than 5000 drug tests. All medal winners were tested, as well as other randomly selected competitors. Suppose that 2% of athletes had actually taken banned drugs. No drug test is perfect. Sometimes the test is positive, indicating that an athlete took drugs, but the athlete actually didn't. We call this a false positive result. Other times, the drug test is negative, but the athlete actually took drugs. This is called a false negative result. Suppose that the testing procedure used at the Olympics has a false positive rate of 1% and a false negative rate of 0.5%. A) Find the probability that a randomly-tested athlete will have a positive test. B) If an athlete has a positive test, what is the probability that they actually use drugs?
Expert Solution
Step 1

The question is about Baye's theorem

Given :

Prop. of athletes taken banned drug = 0.02

False +ve rate = 0.01

False -ve rate = 0.005

 

To find :

A ) Prob. that a randomly selected athlete will have +ve test

B ) If an athlete has + ve test, find the prob. that they actually use drugs

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