Question

On discovering that his family has a 75% risk of heart attack, James took a treadmill test to check his own potential of having a heart attack. The doctors told him that the reliability of the stress test is 70%. What is the probability that James will not have a heart attack and that the test predicts he will?

Answer 1

Answer: The required probability is 0.4375.

Explanation:

Since we have given that

Probability of having risk of heart attack = 75%= 0.75

Probability of having reliability of the stress test = 70%

Probability of not having risk of heart attack =1-0.75 = 0.25

Probability of not having reliability of the stress test = 1-0.70 = 0.30

So, the probability that James will not have a heart attack and that the test predicts he will would be :

P(not having heart attack | correct test) is given by :

`=(0.25* 0.7)/(0.25* 0.7+0.75* 0.3)\\\\=(0.175)/(0.175+0.225)\\\\=(0.175)/(0.4)\\\\=0.4375`

Hence, the required probability is 0.4375.