# 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. - Mathematics

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 and yoga. Interpret the result and state which of the above stated methods is more beneficial for the patient.

#### Solution

Let A, E1, and E2 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(A)=0.40

P(E_1)=P(E_2)=1/2

P(A|E_1)=0.40xx0.70=0.28P(A|E_2)=0.40xx0.75=0.30

Probability that the patient suffering a heart attack followed a course of meditation and yoga is given by P (E1|A).

P(E_1|A)=(P(E_1)P(A|E_1))/(P(E_1)P(A|E_1)+P(E_2)P(A|E_2))

=(1/2xx0.28)/(1/2xx0.28+1/2xx0.30)

=14/29

Let us calculate P(E_2|A)

P(E_2|A)=(P(E_2)P(A|E_2))/(P(E_1)P(A|E_1)+P(E_2)P(A|E_2))

=(1/2xx0.30)/(1/2xx0.28+1/2xx0.30)

=15/29

Since  P(E_1|A)<  P(E_2|A)  the course of yoga and meditation is more beneficial for a person having chances of heart attack.

Concept: Conditional Probability
Is there an error in this question or solution?