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a. Using Bayes' Theorem, if a person tests positive, determine the probability that the person is infected. b. Using Bayes' Theorem, if a person tests negative, determine the probability that the person is not infected.

a. Using Bayes' Theorem, if a person tests positive, determine the probability that the person is infected. b. Using Bayes' Theorem, if a person tests negative, determine the probability that the person is not infected.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 31E
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3.7 Bayes' Rule Theorem of Total Probability or Rule of Elimination If the events B1, B2, ...,BK constitute a partition of the sample space S such that P(Bi) #0 for i = 1,2, ..., k, then for any event A of S, k P(A)= È P(B, )P(A\B,) %3D Bayes' Rule If the events B1, B2, ...,BK Constitute a partition of the sample space S such that P(Bi) #0 for i = 1, 2, ..., k, then for any event A in S such that P(A) # 0, P(B, )P(4\B,) ÈP(B, )P(4|B, ) P(B,|A )= For r= 1, 2, ..., k
Transcribed Image Text:3.7 Bayes' Rule Theorem of Total Probability or Rule of Elimination If the events B1, B2, ...,BK constitute a partition of the sample space S such that P(Bi) #0 for i = 1,2, ..., k, then for any event A of S, k P(A)= È P(B, )P(A\B,) %3D Bayes' Rule If the events B1, B2, ...,BK Constitute a partition of the sample space S such that P(Bi) #0 for i = 1, 2, ..., k, then for any event A in S such that P(A) # 0, P(B, )P(4\B,) ÈP(B, )P(4|B, ) P(B,|A )= For r= 1, 2, ..., k
2) 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 if the person has the virus and 5% of the time if 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, if a person tests positive, determine the probability that the person is infected. b. Using Bayes' Theorem, if a person tests negative, determine the probability that the person is not infected.
Transcribed Image Text:2) 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 if the person has the virus and 5% of the time if 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, if a person tests positive, determine the probability that the person is infected. b. Using Bayes' Theorem, if a person tests negative, determine the probability that the person is not infected.
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