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.

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Chapter1: Combinatorial Analysis
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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.
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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