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?
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?
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section11.8: Probabilities Of Disjoint And Overlapping Events
Problem 2C
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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?
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