Bad gums may mean a bad heart. Researchers discovered that 77%of people who have

Question

Bad gums may mean a bad heart. Researchers discovered that 77%of people who have suffered a heart attack had periodontal disease,an inflammation of the gums. Only 31% of healthy people have thisdisease. Suppose that in a certain community heart attacks arequite rare, occurring with only 12% probability. 1.  If someone has periodontal disease, what is theprobability that he or she will have a heart attack? 2. If 45% of the people in a community will have a heartattack, what is the probability that a person with periodontaldisease will have a heart attack? Bad gums may mean a bad heart. Researchers discovered that 77%of people who have suffered a heart attack had periodontal disease,an inflammation of the gums. Only 31% of healthy people have thisdisease. Suppose that in a certain community heart attacks arequite rare, occurring with only 12% probability. 1.  If someone has periodontal disease, what is theprobability that he or she will have a heart attack? 2. If 45% of the people in a community will have a heartattack, what is the probability that a person with periodontaldisease will have a heart attack?

Explanation / Answer

Given P(D/H)=.77; P(D)=.31; P(H)=.12 1)P(H/D)=P(D/H)P(H)/P(D) =(.77)(.12)/(.31)=.298=.3 2) If P(H)=.45 then P(D/H)=P(H/D)P(D)/P(H) =(.77)(.31)/(.45)=.530 P

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