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 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?

Answer

`14//29`

Explanation

Let `A,E_(1), and E_(2),` respectively, donate the events that a person has a heart attack, the selected person followed the course of yoga and meditation, and the person adopted the durg presripation. Therefore,
`P(A)=0.40`
`P(E_(1))=P(E_(2))=1/2`
`P(A|E_(1))=0.40xx0.70=0.28`
`P(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(E_(1)|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`