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⦁   Suppose in August the Covid-19 situation has calmed down. Since not everyone shows symptoms and...

⦁   Suppose in August the Covid-19 situation has calmed down. Since not everyone shows symptoms and some symptoms could have been a different pneumonia we might use an anti-body test to see if people have had the disease. Let’s assume by August 40% of the US has had the disease. The anti-body test is not perfect. Some people will get “false positives” or “false negatives”. 90% of people who test positive will actually have had the disease. 95% of people who test negative will have not had the disease.

3A) What is the “prior probability” of a random person having had the disease? (That is, before giving the person the test what is your best guess for the likelihood they had the disease?)


3B) If the person receives a positive anti-body test what is the posterior probability of them having had the disease? (That is, what is your best guess for the likelihood they had the disease given they tested positive on the anti-body test?)

3C) If the person receives a negative anti-body test what is the posterior probability of them having had the disease? (That is, what is your best guess for the likelihood they had the disease given they tested negative on the anti-body test?)

Math   Statistics-And-Probability   
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