Suppose 85% of diabetics and 25% of non-diabetics areclassified as diabetic by a

Question

Suppose 85% of diabetics and 25% of non-diabetics areclassified as diabetic by a glucose monitor. Suppose 20% ofthe adult population is diabetic. How many of each type ofperson described would you expect in a population size of 100 1. How many non-diabetics 2. How many Diabetics 3. How many diabetics who are classified bythe glucose monitor as diabetics 4. How many NON-diabetics who are classifed bythe glucose monitor as diabetic 5. How many are classifed as Diabetic by the glucosemonitor(including both diabetic and non-diabetic people) 6. Among the people classified as diabetic bythe monitor, what fraction are acutally diabetic? Suppose 85% of diabetics and 25% of non-diabetics areclassified as diabetic by a glucose monitor. Suppose 20% ofthe adult population is diabetic. How many of each type ofperson described would you expect in a population size of 100 1. How many non-diabetics 2. How many Diabetics 3. How many diabetics who are classified bythe glucose monitor as diabetics 4. How many NON-diabetics who are classifed bythe glucose monitor as diabetic 5. How many are classifed as Diabetic by the glucosemonitor(including both diabetic and non-diabetic people) 6. Among the people classified as diabetic bythe monitor, what fraction are acutally diabetic?

Explanation / Answer

Let S= monitor says diabetic; Let D=diabetic; Will use / for given that in a conditional probability and nfor number. We are given: P(S/D)=.85; P(S/D')=.25; P(D)=.2 andn(population)=100 1)P(D')=1-P(D)=(1-.2)=.8 or n(D')=100(.8)=80 2)P(D)=.2 or n(D) 3)P(S/D)=.85 or n(S/D)=85 4)P(S/D')=.25 or n(S/D')=25 5)P(S)=P(S/D)P(D)+P(S/D')P(D') = .85(.2)+.25(.8)= .37 or 37people 6)P(D/S)=P(S/D)P(D)/P(S) =.85(.2)/.37=.46      

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