Question

Assume that the chances of a patient having a heart attack is 40%. Assuming that a meditation and yoga course reduces the risk of heart attack by 30% and prescription of certain drug reduces its chance 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

Answer 1

Let $A,E_1,E_2$ 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 respectively.

$\therefore P\left(A\right)=0.40$

$P\left(E_1\right)=P\left(E_2\right)=\frac{1}{2}$

$P\left(A/E_1\right)=0.40\times 0.70=028P\left(A/E_2\right)=0.4\times 0.75=0.30$

Probability that the patient suffering a heart attack followed a course of meditation and yoga is given by

$P\left(E_1/A\right)=\frac{P\left(E_1\right)P\left(A/E_1\right)}{P\left(E_1\right)P\left(A/E_1\right)+P\left(E_2\right)P\left(A/E_2\right)}⟹=\frac{\frac{1}{2}\times 0.28}{\frac{1}{2}\times 0.28+\frac{1}{2}\times 0.30}⟹P\left(E_1/A\right)=\frac{14}{29}$