Bad gums may be evidence of a bad heart. Researchers have discovered that 85% of people who have suffered a heart attack had periodontal disease, an inflammation of the gums. Only 29% of healthy people have this disease.
a) Suppose that in a certain community, heart attacks are quite rare, occurring with only 10% probability. If someone has periodontal disease, what is the probability that he or she will have a heart attack?
b) If 40% of the people in a community will have a heart attack, what is the probability that a person with periodontal disease in this community will have a heart attack?
a) We will assume that the statistics above part a) apply to this community. Then let us denote H - heart attack, D - periodontal disease. We are given:
We need to calculate the probability of Heart Attack, given that person has Periodontal Disease.
Using the law of conditional probability:
P(H|D) is what we need to find.
b) Assuming the statistics above the a) are correct for this case. We are given the following:
and we basically need to calculate the same probability as in a) but with different given values:
It can mean either that all people who have Periodontal Disease will have a heart attack or that statistics presented above a) is incorrect.
a) , or
b) 1 or statistics are incorrect