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Assume that 1 out of 270 people in the US are afflicted with a particular disease. There is a test for the disease that is 97% accurate; meaning 3% of the time a person with the disease will get a false negative result and 3% of the time someone without the disease will get a false positive result.
Model this as a sequential game with Nature first deciding who is afflicted with the disease. Second every person gets tested.
A. A person gets a positive test result (the test says they have the disease). First think about what you expect the probability of being sick is given a positive test result. Record your guess before doing any arithmetic. How would the average person on the street probably answer this question? Now find the probability that the person really is sick. What is the probability that the person is not sick?
B. If everyone that tests positive in part A gets tested a second time, now what is the probability that the person is really sick if they received a positive test result?
C. How would your answer change to A and B if we use a country that has a very high infection rate like 26% instead of 1 out of 270?
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