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Jimmy is being tested for a disease called conditionitis, a medical condition that afflicts 1% of the population. The test result is positive, i.e., the

Jimmy is being tested for a disease called conditionitis, a medical condition that afflicts 1% of the population. The test result is positive, i.e., the test claims that Jimmy has the disease. Let D be the event that Jimmy has the disease and T be the event that he tests positive. Suppose that the test is ''95% accurate"; there are different measures of the accuracy of a test, but in this problem it is assumed to mean that P(T|D)=0.95 and P(Tc |Dc )=0.95. The quantity P(T|D) is known as the sensitivity or true positive rate of the test, and P(Tc |Dc ) is known as the specificity or true negative rate. Find the conditional probability that Jimmy has conditionitis, given the evidence provided by the test result.

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