A certain virus infects one in every 300 people. A test used to detect the virus in a person is positive 90% 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, 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 Click the icon to the right to review Bayes' Theorem. (a) The probability that a person is infected when a person tests positive is 0.057 (Do not round until final answer. Then round to three decimal places as needed.) (b) The probability that a person is not infected when a person tests negative is (Round to four decimal places as needed.)

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section9.2: Probability
Problem 39E: Spinner A and B shown in the figure are spun at the same time. (a) Are the events "spinner A stops...
icon
Related questions
Topic Video
Question
100%

How do I solve this? I have no idea where to beging. My class is online so I'm litteraly teaching myself and I can not figure this one out.

A certain virus infects one in every 300 people. A test used to detect the virus in a person is positive 90% 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, 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
Click the icon to the right to review Bayes' Theorem.
(a) The probability that a person is infected when a person tests positive is 0.057
(Do not round until final answer. Then round to three decimal places as needed.)
(b) The probability that a person is not infected when a person tests negative is
(Round to four decimal places as needed.)
Transcribed Image Text:A certain virus infects one in every 300 people. A test used to detect the virus in a person is positive 90% 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, 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 Click the icon to the right to review Bayes' Theorem. (a) The probability that a person is infected when a person tests positive is 0.057 (Do not round until final answer. Then round to three decimal places as needed.) (b) The probability that a person is not infected when a person tests negative is (Round to four decimal places as needed.)
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 5 steps with 4 images

Blurred answer
Knowledge Booster
Propositional Calculus
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Recommended textbooks for you
College Algebra
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage