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An observational study investigates the connection between aspirin use and three vascular conditions - gastrointestinal bleeding, primary stroke, and cardiovascular disease - using a group of patients exhibiting these disjoint conditions with the following prior probabilities: P(GI bleeding) = 0.2, P(Stroke) = 0.3, and P(CVD) = 0.5, as well as with the following conditional probabilities: P(Aspirin | GI bleeding) = 0.09, P(Aspirin | Stroke) = 0.04, and P(Aspirin | CVD) = 0.02.
(a) Calculate the following posterior probabilities: P(GI bleeding | Aspirin), P(Stroke | Aspirin), and P(CVD | Aspirin).
(b) Interpret: Compare the prior probability of each category with its corresponding posterior probability. What conclusions can you draw? Be as specific as possible.
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