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Covid Bayes' Theorem

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Part 1. Covid infection rates on the GW campus are currently at 2%. You have not left campus in several weeks. Moreover, you have no symptoms and haven't been in contact with any infected individuals, but you take a rapid antigen test and it shows a positive reading. This particular test has a false positive rate of 5% and a 10% false negative rate.

What is the probability of your being Covid infected given the positive test result?

Part 2. After having determining the posterior probability in this instance, you decide to take another rapid antigen test from a different manufacturer that has a false positive rate of 10% and false negative rate of 5%? It also results in a positive reading.

What is the probability of your being Covid infected given the second positive test result?

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Solution Summary

All necessary terms have been assigned. Step-by-step work showing how to set up the equation for Bayes' Theorem is shown. All calculations are shown. A file showing calculator work is provided.

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Part 1.


Let C = the event that you have Covid.
Let Pos = the event that you test positive.
Let Neg = the event that you test negative.


Step 1) State the given information.
P(C) = 0.02
P(False Positive) = P(Pos | No C) = 0.05
P(False Negative) = P(Neg | C) = 0.1

Step 2) Find P(No C)
P(No C) = 1 - P(C)
= 1 - 0.02
= ...

Solution provided by:
  • MSc, California State Polytechnic University, Pomona
  • MBA, University of California, Riverside
  • BSc, California State Polytechnic University, Pomona
  • BSc, California State Polytechnic University, Pomona
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