Course Notes - Department of Mathematics and Statistics

Fred’s DayShould Fred be worried about returning a positive test result? Whatis the likelihood he has the disease?Remember that the prevalence of his disease is 1 in 10000 and theprobability that the diagnostic test returns a positive result is 95% whenpeople have the disease, and 6% of cases when people don’t have thedisease. We learned during this section that conditional probabilitiesare not necessarily reversible, so the probability that one has a diseasegiven they have a positive test result (what we currently have) is notthe same as the probability of having a positive test result given onehas the disease (what we wish to know). The first step would be tosummarize our information using a tree diagram. (For this diagram T= Test Positive, and D = Has disease)From this tree diagram it is easy to see the total probability of gettinga positive test is 0.0599 (False positive) + 0.000095 (True Postive) =0.059995. Therefore as we have learned it is just a matter of dividingthe probability of a true positive by the probability of getting a positivetest, to find the probability of Fred having the disease given he has apositive test result.57