1) False positives/negatives: A certain deadly disease occurs in 1 percent of the population

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1) False positives/negatives: A certain deadly disease occurs in 1 percent of the population. A blood test for this disease has a 2 percent false positive rate, and a 5 percent false negative rate (i.e., 2 percent of those not having the disease test positive, and 5 percent of those having the disease test negative). Suppose you want to put your mind at ease and take the blood test.

 

(a) If you test positive, how certain can you be that you actually have the disease?

 

(b) If you test negative, how certain can you be that you do not have the disease?

 

Hints: Work with the events P= "test positive", N = "test negative", D = "has disease." Use the complement rule for conditional probabilities and Bayes' Rule.