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
![P(B|A) = \frac{P(A \cap B)}{P(A)}](https://tex.z-dn.net/?f=P%28B%7CA%29%20%3D%20%5Cfrac%7BP%28A%20%5Ccap%20B%29%7D%7BP%28A%29%7D)
In which
P(B|A) is the probability of event B happening, given that A happened.
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
![P(A) = 0.2*0.1 + 0.3*0.9 = 0.29](https://tex.z-dn.net/?f=P%28A%29%20%3D%200.2%2A0.1%20%2B%200.3%2A0.9%20%3D%200.29)
Intersection of A and B:
Not having the disease, suffering a heart attack, so 20% of 10%.
![P(A cap B) = 0.2*0.1 = 0.02](https://tex.z-dn.net/?f=P%28A%20cap%20B%29%20%3D%200.2%2A0.1%20%3D%200.02)
What is the probability that he or she will have a heart attack?
![P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.02}{0.29} = 0.069](https://tex.z-dn.net/?f=P%28B%7CA%29%20%3D%20%5Cfrac%7BP%28A%20%5Ccap%20B%29%7D%7BP%28A%29%7D%20%3D%20%5Cfrac%7B0.02%7D%7B0.29%7D%20%3D%200.069)
0.069 = 6.9% probability that he or she will have a heart attack