3.) Suppose that a medical test has a 92% chance of detecting adisease if the pe

Question

3.) Suppose that a medical test has a 92% chance of detecting adisease if the person has
it (i.e., 92% sensitivity) and a 94% chance of correctly indicatingthat the disease is
absent if the person really does not have the disease (i.e., 94%specificity). Suppose 10%
of the population has the disease. A.) What is the probability thata randomly chosen
person will test positive? B.) Suppose that a randomly chosenperson does test positive.
What is the probability that this person really has thedisease?

Explanation / Answer

A. There are two possibilities: You test positive and you havethe disease OR you test positive and you don't have thedisease. Add these probabilities together and you get theanswer to a... = (0.1)(0.92) + (0.9)(0.06) = 0.146 -- B. This is a conditional probability. Namely, P(DiseaseGIVEN positive) = P(Disease AND Positive) / P(positive) = 0.092 / 0.146 = 0.630

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