Bad gums may mean a bad heart. Researchers discovered that 81% of people who hav

Question

Bad gums may mean a bad heart. Researchers discovered that 81% of people who have suffered a heart attack had periodontal disease, an inflammation of the gums. Only 26% of healthy people (no heart attack) have this disease. Suppose that in a certain community heart attacks are quite rare, occurring with only 10% probability.

A. If someone has periodontal disease, what is the probability that he or she will have a heart attack?

B. If 39% of the people in a community will have a heart attack, what is the probability that a person with periodontal disease will have a heart attack?

Explanation / Answer

A)P(heart attacks) = 0.10

P(he or she will have a heart attack/periodontal disease)

= P(he or she will have a heart attack and periodontal disease)/P(periodontal disease)

P(he or she will have a heart attack and periodontal disease) = 0.1*0.81 = 0.081

P(periodontal disease) = 0.1*0.81+0.9*0.26 = 0.315

P(he or she will have a heart attack/periodontal disease)

= P(he or she will have a heart attack and periodontal disease)/P(periodontal disease)

= 0.081/0.315 = 0.257

B)

P(heart attacks) = 0.39

P(he or she will have a heart attack/periodontal disease)

= P(he or she will have a heart attack and periodontal disease)/P(periodontal disease)

P(he or she will have a heart attack and periodontal disease) = 0.39*0.81 = 0.3159

P(periodontal disease) = 0.39*0.81+0.61*0.26 = 0.4745

P(he or she will have a heart attack/periodontal disease)

= P(he or she will have a heart attack and periodontal disease)/P(periodontal disease)

= 0.3159/0.4745 = 0.6657

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