Bad gums may mean a bad heart. Researchers discovered that 81% of people who have suffered a heart attack has periodontal disease, an inflammation of the gums. Only 30% of healthy people have this disease. Suppose that in a certain community heart attacks are quite rare, occurring with only 15% probability.

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

0.405 or 40.5%

Step-by-step explanation:

Let event A=having a periodontal disease

event B=having a heart attack

we are given

P (A) = P (having a periodontal disease) = 0.30

P (B) = P (having a heart attack) = 0.15

P (A/B) = P (have a periodontal disease/have a heart attack) = 0.81

P (B/A) = P (have a heart attack/have a periodontal disease) = ?

P (A/B) = P (A∩B) / P (B)

P (A∩B) = P (B) * P (A/B) = 0.15*0.81=0.1215

P (B/A) = P (A∩B) / P (A) = 0.1215/0.3=0.405

There is 40.5% probability that if someone has periodontal disease will have a heart attack.