diagnosis. (10 pts) b. What is the probability that a patient will be referred f
ID: 3359543 • Letter: D
Question
diagnosis. (10 pts) b. What is the probability that a patient will be referred for further lab test? A certain virus infects five in every 400 people. A test used to detect the virus in a person is positive 85% of the time when the person has the virus and 8% of the time when the person does not have the virus. Let A be the event "the person is infected" and B be the event "the person tests positive." (20 pts 2 Using Bayes' Theorem, when a person tests positive, determine the probability that the person is infected Using Bayes' Theorem, when a person tests negative, determine the probability that a person is not infected a. b.Explanation / Answer
A) P(A) = 5/400 = 0.0125
P(B) = 0.0125 * 0.85 + ( 1 - 0.0125) * 0.08 = 0.0896
P(A|B) = P(B|A) * P(A)/P(B)
= 0.85 * 0.0125 / 0.0896
= 0.1186
B) P(A') = 1 - 0.0125 = 0.9875
P(B') = 1 - 0.0896 = 0.9104
P(A'|B') = P(B'|A') * P(A')/P(B')
= (1 - 0.08) * 0.9875/0.9104 = 0.9979
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.