Question

Bad gums may mean a bad heart. Researchers discovered that 82% of people who have suffered a heart attack had periodontal disease, an inflammation of the gums. Only 33% of healthy people have this disease. Suppose that in a certain community heart attacks are quite rare, occurring with only 15% probability. A. If someone has periodontal disease, what is the probability that he or she will have a heart attack

Answer 1

37.27% probability that he or she will have a heart attack.

Explanation:

Bayes Theorem:

Two events, A and B.

`P(B|A) = (P(B)*P(A|B))/(P(A))`

In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.

In this question:

Event A: Periodontal disease

Event B: Heart attack

Researchers discovered that 82% of people who have suffered a heart attack had periodontal disease, an inflammation of the gums.

This means that
`P(A|B) = 0.82`

Only 33% of healthy people have this disease.

This means that
`P(A) = 0.33`

Suppose that in a certain community heart attacks are quite rare, occurring with only 15% probability.

This means that
`P(B) = 0.15`

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

`P(B|A) = (0.15*0.82)/(0.33) = 0.3727`

37.27% probability that he or she will have a heart attack.