A drug-screening test is used in a large population of people of whom 7% actually use drugs. Suppose that the false positive rate is 2% and the false negative rate is 3%. Thus, a person who uses drugs tests positive for them 97% of the time, and a person who does not use drugs tests negative for them 98% of the time. (Round your answers to one decimal place.) To answer the following questions, let A be the event that a randomly chosen person tests positive for drugs, let B, be the event that a randomly chosen person uses drugs, and let B, be the event that a randomly chosen person does not use drugs. Then A° is the event that a randomly chosen person does not test positive for drugs. Now, as percents, %, P(A | B2) = | %, P(B2) = %, and % and P(A° | B2) = P(B,) = P(A° | B,) = %. Hence, P(A | B,) = %. (a) What is the probability (as a %) that a randomly chosen person who tests positive for drugs actually uses drugs? The probability that a randomly chosen person who tests positive for drugs actually uses drugs is -Select-- When Bayes' theorem is used to evaluate this quantity, the result, as a percent, is %. (b) What is the probability (as a %) that a randomly chosen person who tests negative for drugs does not use drugs? %
A drug-screening test is used in a large population of people of whom 7% actually use drugs. Suppose that the false positive rate is 2% and the false negative rate is 3%. Thus, a person who uses drugs tests positive for them 97% of the time, and a person who does not use drugs tests negative for them 98% of the time. (Round your answers to one decimal place.) To answer the following questions, let A be the event that a randomly chosen person tests positive for drugs, let B, be the event that a randomly chosen person uses drugs, and let B, be the event that a randomly chosen person does not use drugs. Then A° is the event that a randomly chosen person does not test positive for drugs. Now, as percents, %, P(A | B2) = | %, P(B2) = %, and % and P(A° | B2) = P(B,) = P(A° | B,) = %. Hence, P(A | B,) = %. (a) What is the probability (as a %) that a randomly chosen person who tests positive for drugs actually uses drugs? The probability that a randomly chosen person who tests positive for drugs actually uses drugs is -Select-- When Bayes' theorem is used to evaluate this quantity, the result, as a percent, is %. (b) What is the probability (as a %) that a randomly chosen person who tests negative for drugs does not use drugs? %
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Transcribed Image Text:A drug-screening test is used in a large population of people of whom 7% actually use drugs. Suppose that the false
positive rate is 2% and the false negative rate is 3%. Thus, a person who uses drugs tests positive for them 97% of the
time, and a person who does not use drugs tests negative for them 98% of the time. (Round your answers to
one decimal place.)
To answer the following questions, let A be the event that a randomly chosen person tests positive for drugs, let B, be the
event that a randomly chosen person uses drugs, and let B, be the event that a randomly chosen person does not use
drugs. Then A is the event that a randomly chosen person does not test positive for drugs. Now, as percents,
P(B,) =
%, P(B,) =
%, P(A | B,) =
%, and
P(A° | B,) =
%. Hence, P(A | B,) =
% and P(A° | B2)
%.
(a) What is the probability (as a %) that a randomly chosen person who tests positive for drugs actually uses drugs?
The probability that a randomly chosen person who tests positive for drugs actually uses drugs is -Select--- v
When Bayes' theorem is used to evaluate this quantity, the result, as a percent, is
%.
(b) What is the probability (as a %) that a randomly chosen person who tests negative for drugs does not use drugs?
Transcribed Image Text:tests positive for drugs actually uses drugs?
drugs actually uses drugs is ---Select---
a percent, is
-Select-
P(A| B:)
P(A| B:)
tests negative for drugs does P(B: |A)
P(B: |A)
gs?
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