Let A, ${\mathit{E}}_1$, and ${\mathit{E}}_2$, respectively denote the events that a person has a heart attack, the selected person followed the course of yoga and meditation, and the person adopted the drug prescription.
∴ P (A) = 0.40
P $\left({\mathit{E}}_1\right)$ = P $\left({\mathit{E}}_2\right)$ = $\frac{1}{2}$
P (A|${\mathit{E}}_1$) = 0.40 × 0.70 = 0.28
P (A|${\mathit{E}}_2$) = 0.40 × 0.75 = 0.30
Probability that the patient suffering a heart attack followed a course of meditation and yoga = P (${\mathit{E}}_1$|A)
=
= $\frac{\frac{1}{2}\times 0.28}{\frac{1}{2}\times 0.28+\frac{1}{2}\times 0.30}$
= $\frac{28}{28+30}$
= $\frac{28}{58}$
= $\frac{14}{29}$
Now, calculate P (${\mathit{E}}_2$|A)
P (${\mathit{E}}_2$|A) =
= $\frac{\frac{1}{2}\times 0.30}{\frac{1}{2}\times 0.28+\frac{1}{2}\times 0.30}$
= $\frac{30}{28+30}$
= $\frac{30}{58}$
= $\frac{15}{29}$
Since P (${\mathit{E}}_1$|A) < P (${\mathit{E}}_2$|A), the course of yoga and meditation is more beneficial for a patient.