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Sagot :
Answer:
A. 0.099
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: She does not have a heart attack.
Event B: tests predicts that she will have a heart attack
The doctors told her that the reliability of the stress test is 67%.
This means that there is a 100 - 67 = 33% of not having a heart attack if the test predicts she will have a heart attack, so:
[tex]P(B|A) = 0.33[/tex]
70% risk of heart attack
So 100 - 70 = 30% probability of not having a heart attack, which means that [tex]P(A) = 0.3[/tex]
What is the probability that Erin will not have a heart attack and the test predicts that she will?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
[tex]P(A \cap B) = P(B|A)*P(A) = 0.33*0.3 = 0.099[/tex]
The correct answer is given by option A.
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