Question

Assume that the chances of a patient having a heart attack is 40%. It is also assumed that a meditation and yoga course reduce the risk of heart attack by 30% and prescription of certain drug reduces its chances by 25%. At a time a patient can choose any one of the two options with equal probabilities. It is given that after going through one of the two options the patient selected at random suffers a heart attack. Find the probability that the patient followed a course of meditation and yoga?

Answer 1

Let $A,E_1$, and $E_2$ 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.
$\therefore P\left(A\right)=0.40$
$P\left(E_1\right)=P\left(E_2\right)=\frac{1}{2}$
$P\left(A|E_1\right)=0.40\times 0.70=0.28$
$P\left(A|E_2\right)=0.40\times 0.75=0.30$
Probability that the patient suffering a heart attack followed a course of meditation and yoga is given by $P\left(E_1|A\right)$.
$P\left(E_1|A\right)=\frac{P\left(E_1\right)P\left(A|E_1\right)}{P\left(E_1\right)P\left(A|E_1\right)+P\left(E_2\right)P\left(A|E_2\right)}$
$=\frac{\frac{1}{2}\times 0.28}{\frac{1}{2}\times 0.28+\frac{1}{2}\times 0.30}$
$=\frac{14}{29}=0.48$