3.45 Write the event a patient has an illness as T. Write the event that a test reports the patient has the illness as R. Assume that P(R|T°) = 0.1. We have that P(Z|R) = 0.5. (a) Compute P(T) as a function of P(R|T), and plot it. (b) What is the smallest possible value of P(T)? For what value of P(R|T) does this occur? (c) Now plot the smallest possible value of P(I) for different values of P(R|T°), assuming that P(R|T) = 0.99.
3.45 Write the event a patient has an illness as T. Write the event that a test reports the patient has the illness as R. Assume that P(R|T°) = 0.1. We have that P(Z|R) = 0.5. (a) Compute P(T) as a function of P(R|T), and plot it. (b) What is the smallest possible value of P(T)? For what value of P(R|T) does this occur? (c) Now plot the smallest possible value of P(I) for different values of P(R|T°), assuming that P(R|T) = 0.99.
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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![3.45 Write the event a patient has an illness as T. Write the event that a test reports the patient has the illness as R. Assume
that P(R|T°) = 0.1. We have that P(I|R) = 0.5.
(a) Compute P(I) as a function of P(R|T), and plot it.
(b) What is the smallest possible value of P(T)? For what value of P(R|T) does this occur?
(c) Now plot the smallest possible value of P(T) for different values of P(R|T°), assuming that P(R|T) = 0.99.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F47a369e8-57e2-40e5-9d83-f84bcb97f998%2Fb7f3905b-8f4d-4d49-b129-164de3344597%2F88bgr_processed.png&w=3840&q=75)
Transcribed Image Text:3.45 Write the event a patient has an illness as T. Write the event that a test reports the patient has the illness as R. Assume
that P(R|T°) = 0.1. We have that P(I|R) = 0.5.
(a) Compute P(I) as a function of P(R|T), and plot it.
(b) What is the smallest possible value of P(T)? For what value of P(R|T) does this occur?
(c) Now plot the smallest possible value of P(T) for different values of P(R|T°), assuming that P(R|T) = 0.99.
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