Answer:
0.069 = 6.9% probability that he or she will have a heart attack
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Does not have periodontal disease
Event B: Has a heart attack.
Probability of not having a periodontal disease:
100 - 80 = 20% of 10%(had a heart attack).
30% of 100-10 = 90%(did not have a heart attack). So
[tex]P(A) = 0.2*0.1 + 0.3*0.9 = 0.29[/tex]
Intersection of A and B:
Not having the disease, suffering a heart attack, so 20% of 10%.
[tex]P(A cap B) = 0.2*0.1 = 0.02[/tex]
What is the probability that he or she will have a heart attack?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.02}{0.29} = 0.069[/tex]
0.069 = 6.9% probability that he or she will have a heart attack
