3. You are diagnosed with an uncommon disease. You know that among the general population there is a 3% chance of getting it. Use the letter D for the event "you have the disease" and T for the "the test says so." It is known that the test is imperfect: Pr(T|D) = 0.90 and Pr(TC | DC) = 0.95. (a) Given that you test positive (the test is positive if you have the disease), what is the probability that you really have the disease?

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