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Reliability of Testing A certain virus infects one in
Chapter 3, Problem 37EC(choose chapter or problem)
Problem 37EC
Reliability of Testing A certain virus infects one in every 200 people. A test used to detect the virus in a person is positive 80% of the time when the person has the virus and 5% of the time when the person does not have the virus. (This 5% result is called a false positive.) Let A be the event “the person is infected” and B be the event “the person tests positive.”
(a) Using Bayes’ Theorem, when a person tests positive, we determine the probability that the person is infected
(b) Using Bayes’ Theorem, when a person tests negative, determine the probability that the person is not infected.
Questions & Answers
QUESTION:
Problem 37EC
Reliability of Testing A certain virus infects one in every 200 people. A test used to detect the virus in a person is positive 80% of the time when the person has the virus and 5% of the time when the person does not have the virus. (This 5% result is called a false positive.) Let A be the event “the person is infected” and B be the event “the person tests positive.”
(a) Using Bayes’ Theorem, when a person tests positive, we determine the probability that the person is infected
(b) Using Bayes’ Theorem, when a person tests negative, determine the probability that the person is not infected.
ANSWER:
Solution:
Step 1 of 3:
It is given that one in every 200 persons is infected by certain type of virus.
80% of the time the test gives positive result when the person has virus and 5% of the time the test gives positive result when the person is not infected by the person.
Also, it is given that A denotes the event that the person is infected and B denotes the event that the person tests positive.
Using this we need to obtain the required values.