Assume the probability of contracting COVID-19 is 0.09 (p(C = 1) = 0.09). Assume the probability of COVID antibody test of a person becomes positive given the person has COVID-19 is 0.90 (p(T = 1|C = 1) = 0.9) and the probability of COVID antibody test of a person becomes negative given the person does not have COVID-19 is 0.99 (p(T=0C = 0) = 0.99). What is the probability of a person having COVID-19 given his/her antibody test is positive (p(C = 1 |T = 1))? Hint: You need to use the Bayes rule. Show all of your calculations.

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