Answer: The required probability is 0.4375.
Step-by-step 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 :
[tex]=\dfrac{0.25\times 0.7}{0.25\times 0.7+0.75\times 0.3}\\\\=\dfrac{0.175}{0.175+0.225}\\\\=\dfrac{0.175}{0.4}\\\\=0.4375[/tex]
Hence, the required probability is 0.4375.
