Suppose we know the prevalence of covid in a region and the sensitivity and Specificity of a rapid covid test. The details are given as follows: • prevalence: P(covid)=0.01 • sensitivity: P(positive test | covid)= 0.9 • specificity: P(negative test | no covid)=0.8 Use the information above to answer the following questions. (a) Find P(positive test). (b) If a student got a positive test, conditional on this information, what was the probability that the student had covid? (c) Which theorem did you use to solve part (b)? Briefly describe the theorem.

MATLAB: An Introduction with Applications
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Suppose we know the prevalence of covid in a region and the sensitivity and Specificity of a
rapid covid test. The details are given as follows:
• prevalence: P(covid)=0.01
• sensitivity: P(positive test | covid)= 0.9
• specificity: P(negative test | no covid)=0.8
Use the information above to answer the following questions.
(a) Find P(positive test).
(b) If a student got a positive test, conditional on this information, what was the probability
that the student had covid?
(c) Which theorem did you use to solve part (b)? Briefly describe the theorem.
Transcribed Image Text:Suppose we know the prevalence of covid in a region and the sensitivity and Specificity of a rapid covid test. The details are given as follows: • prevalence: P(covid)=0.01 • sensitivity: P(positive test | covid)= 0.9 • specificity: P(negative test | no covid)=0.8 Use the information above to answer the following questions. (a) Find P(positive test). (b) If a student got a positive test, conditional on this information, what was the probability that the student had covid? (c) Which theorem did you use to solve part (b)? Briefly describe the theorem.
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