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

Answer:

the probability that Erin won't have a heart attack and the test predicts that she will is 0.4653 (aka 46.53%)

Step-by-step explanation:

For this conditional probability problem, you will need to use Bayes theorem.  When you put the values in (like below) you get 0.4653.

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 .

$P(A\cap B)=P(A).P(B)\\\\P(A\cap B)=0.70\times 0.67\\\\P(A\cap B)=0.469\\\\P(A\cap B)=0.469\times 100\%\\\\P(A\cap B)=46.9\%$

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