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Before testing for COVID, Joan has a prior probability of 0.35 of having COVID. If Joan has COVID, there is a probability of 0.99 that

Before testing for COVID, Joan has a prior probability of 0.35 of having COVID. If Joan has COVID, there is a probability of 0.99 that the test would come positive and a probability of 0.01 that the test would come out negative. If Joan does not have COVID, there is a probability of 0.2 that the test would come positive and a probability of 0.8 that the test would come out negative. Multiple tests provide independent information. Joan takes two tests. The first test comes out negative and the second test comes out positive. What is the posterior odds-ratio of this outcome?

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