Question

On discovering that her family had a 70% risk of heart attack, Erin took a treadmill test to check her own potential of having a heart attack. The doctors told her that the reliability of the stress test is 67%. What is the probability that Erin will have a heart attack and the test predicts it?

Answer 1

The probability that Erin will have a heart attack and the test predicts it is 46.9%.

Step-by-step explanation:

To find the probability that Erin will have a heart attack and the test predicts it, we need to multiply the probability of Erin having a heart attack (the family risk of 70%) with the reliability of the stress test (67%).

Probability of having a heart attack = 70% = 0.70

Reliability of the stress test = 67% = 0.67

Probability of Erin having a heart attack and the test predicting it = 0.70 * 0.67 = 0.469 (or 46.9%)

Answer 2

Answer: There is probability of 46.9% that Erin will have a heart attack and the test predicts it.

Step-by-step explanation:

Since we have given that

Probability that her family had a risk of heart attack P(A)= 70%

Probability that the reliability of the stress test P(B)= 67%

Since events A and B are independent events.

so, we can apply the rule of independent events :

We need to find the probability that Erin will have a heart attack and the test predicts it .

`P(A\cap B)=P(A).P(B)\\\\P(A\cap B)=0.70* 0.67\\\\P(A\cap B)=0.469\\\\P(A\cap B)=0.469* 100\%\\\\P(A\cap B)=46.9\%`

Hence, there is probability of 46.9% that Erin will have a heart attack and the test predicts it.